International Journal Of Nonlinear Analysis And Applications
Volume:12 Issue: 1, Winter-Spring 2021

In this paper, we establish the existence and uniqueness of common coupled fixed point results for three covariant mappings in bipolar metric spaces. Moreover, we give an illustration which presents the applicability of the achieved results also we provided applications to homotopy theory as well as integral equations.

In this paper, a real-time denoising filter based on modelling of stable hybrid models is presented. The hybrid models are composed of the shearlet filter and the adaptive Wiener filter in different forms. The optimization of various models is accomplished by the genetic algorithm. Next, regarding the significant relationship between Optimal models and input images, changing the structure of Optimal models for image denoising is modelled by the ANFIS. The eight hundred digital images are used as train images. For eight hundred training images, Sixty seven models are found. For integrated evaluation, the amounts of image attributes such as Peak Signal to Noise Ratio, Signal to Noise Ratio, Structural Similarity Index, Mean Absolute Error and Image Quality Assessment are evaluated by the Fuzzy deduction system. Finally, for the features of a sample noisy image as test data, the proposed denoising model of ANFIS is compared with wavelet filter in 2 and 4 level , Fast bilateral filter, TV-L1, Median, shearlet filter and the adaptive Wiener filter. In addition, run time of proposed method are evaluated. Experiments show that the proposed method has better performance than others.

In this work, we consider variable order difusion and wave equations. The derivative is described in the Caputo sence of variable order. We use the Genocchi polynomials as basic functions and obtain operational matrices via these polynomials. These matrices and collocation method help us to convert variable order diffusion and wave equations to an algebraic system. Some examples are given to show the validity of the presented method.

In this manuscript, we investigate solutions of the partial differential equations (PDEs) arising in mathematical physics with local fractional derivative operators (LFDOs). To get approximate solutions of these equations, we utilize the reduce differential transform method (RDTM) which is based upon the LFDOs. Illustrative examples are given to show the accuracy and reliable results. The obtained solutions show that the present method is an efficient and simple tool for solving the linear and nonlinear PDEs within the LFDOs.

The Internet of Things (IoT) is an emerging phenomenon in the field of communication, in which smart objects communicate with each other and respond to user requests. The IoT provides an integrated framework providing interoperability across various platforms. One of the most essential and necessary components of IoT is wireless sensor networks. Sensor networks play a vital role in the lowest level of IoT. Sensors in sensor networks use batteries which are not replaceable, and hence, energy consumption becomes of great importance. For this reason, many algorithms have been recently proposed to reduce energy consumption. In this paper, a meta-heuristic method called whale optimization algorithm(WOA) is used to clustering and select the optimal cluster head in the network. Factors such as residual energy, shorter distance, and collision reduction have been considered to determine the optimal cluster head. To prove the optimal performance of the proposed method, it is simulated and compared with three other methods in the same conditions. It outperforms the other methods in terms of energy consumption and the number of dead nodes.

This paper presents a linkage factors synthesis and multi-level optimization technique for bi-stable compliant mechanism. The linkage synthesis problem is modeled as multiple level factors and responses optimization problem with constraints. The bi-stable compliant mechanism is modeled as a crank slider mechanism using pseudo-rigid-body model (PRBM). The model exerts the large deflection of flexible element which explains compliant mechanism’s bi-stable performance. The design concept is applied on variable input parameters subsets. Though the effect of compliant mechanism process factors on Fmax and PRBM deflection angle (Theta-cap Θ1) are contradictory when studied individually as no response gives best process quality. The relationship model between input factors and responses characteristics were generated by ANOVA and optimized by response surface methodology (RSM). ANOVA shown more significant factors are the initial angle of link1 (θ1) and material thickness (t). The Box-Behnken design of RSM is applied with a desirability function approach to determine the optimum set of parameters for minimizing Fmax and maximizing the Theta-cap (Θ1). Thus, this technique shown flexibility based on the product application could be tested and established.

This study intends to examine the relationship between investment efficiency and financial information excellence. The study is also examining the moderating impact of sustainability on the relation between excellence in financial information and investment productivity.

The cumulative measurements are 668 firm-years and are made up of 257 subsamples of underinvestment and 411 sub-samples of overinvestment. This study may find no proof on the moderating effect of diversification on the relation between excellence in financial information and efficiency in investment. In the years 2016 to 2019, our samples are companies listed on the Dhaka Stock Exchange.

 The results indicate that financial information reporting quality (both for overinvestment and underinvestment sub-samples) has a positive association with investment performance. Although the evidence is not consistent across sub-samples, the test findings on the relationship between diversification and efficiency of investment appear to indicate a negative and substantial relationship between diversification and efficiency of investment. Research limitations/implications – The study finds no research investigating financial information quality and the productivity of investments. Moreover, it also discusses the regulating consequence for diversification on the correlation concerning financial knowledge and productivity of investment, which has not been examined in current studies as well.

This research fills a void in the literature by providing understandings into performs followed by Bangladeshi companies in diversification effects in investment productivity.This study also has major consequences in providing additional proof of the connection between financial information and productivity of investment.

By definition, web-services composition works on developing merely optimum coordination among a number of available web-services to provide a new composed web-service intended to satisfy some users requirements for which a single web service is not (good) enough. In this article, the formulation of the automatic web-services composition is proposed as several set-cover problems and an approximation algorithm has been exploited to solve them. In proposed method, the web-service composition has been carried out within two main phases, the top-down expansion of the composition tree, and the production of composed service by bottom-up traversal of composition tree. In the first phase, the production of a composition tree (similar to the production of tree in problemsolving by searching) is proposed by starting from the output or post-conditions of the requested service towards its input or pre-conditions. Each node or state of the tree is a set of inputs and/or outputs or conditions, and services as tree edges illustrate the transition from one node to another. In the second phase, finding the path from the leaves of the produced composition tree to the root is considered equal to reaching the output of requested service, and this path specifies the involved services and the composition plan. The requested service input set determines the available leaves of the composition tree. To achieve each non-leaf node of the tree, a set-cover problem is produced and solved using a greedy approximation algorithm. If the production and solving of the set-cover problems continues hierarchically until it reaches the root node, the composition plan and cost of the required composition service will be specified. The main focus of this research is the joint sequential and parallel composition with the aim of producing near-optimal and QoS-aware composed services.

In this study two actual types of problems are considered and solved: 1) determining the maximum common connected fragment of the T-tree (T-directed tree) which does not change with time; 2) determining all non-isomorphic maximum common connected fragments of the T-tree (T-directed tree) which do not change with time. The choice of the primary study of temporal directed trees and trees is justified by the wide range of their practical applications. Effective methods for their solution are proposed. Examples of the solution of the problem for temporal trees and temporal directed trees are given. It is shown that the experimental estimates of the computational complexity of the solution for problems of the temporal directed trees and the temporal trees.

In this paper, we prove the existence of a random fixed point of by using pointwise asymptotically nonexpansive random operator and the stability resultsof two iterative schemes for random operator.

In this paper, we first derive specific results concerning the continuity and upper semi-continuity of the spectral radius and spectrum functions on fundamental locally multiplicative topological algebras. We continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms in these algebras.

In this paper, we employed fuzzy transforms to present a new method for solving the problem through second-order fuzzy initial value. The advantage of the fuzzy transform method is that, unlike other methods (e.g. high-order fuzzy Taylor series), it does not require any higher-order derivative calculation, thus reducing computational cost. In two examples, the results of the newly proposed method were examined against several conventional methods, indicating the more desirable performance of the new method.

A Location-Arc Routing Problem (LARP) is a practical problem, while a few mathematical programming models have been considered for this problem. In this paper, a mixed non-linear programming model is presented for a multi-period LARP with the time windows under demand uncertainty. The time windows modeling in the arc routing problem is rarely. To the best our knowledge, it is the first time that the robust LARP model is verified and an optimal solution is presented for it. For this purpose, the CPLEX solver is used for solving the treasury location problems of a bank as a case study. These problems are node-based with close nods and can be transformed into arc-based. Therefore, the method LRP and LARP models can be used to solve these problems. The comparing results of the LRP and LARP models prove that the LARP has a better performance regarding timing and optimal solution. Furthermore, comparing the results of deterministic and robust LARP models for this case study shows the validity of the robust optimization approach.

In this study, we use game theory to analyze the current situation of Iran and the United States as a result of the US withdrawal from the Comprehensive Plan of Action and the imposition of finanancial and oil sanctions on Iran and Iran's resilience to these sanctions. We also present an oil strategy, as a credible threat, that helps Iran to get out of the sanctions.

In this paper, we establish some new variants of the Hermite--Hadamard integral type inequalities for functions whose $n$th derivatives in absolute values at certain powers are strongly $eta$-convex.

Parameter recovery of dynamical systems has attracted much attention in recent years. The proposed methods for this purpose can not be used in real-time applications. Besides, little works have been done on the parameter recovery of the fractional dynamics. Therefore, in this paper, a convolutional neural network is proposed for parameter recovery of the fractional dynamics. The presented network can also estimate the uncertainty of the parameter estimation and has perfect robustness for real-time applications.

‎In this paper‎, ‎we study the following nonautonomous rational difference equation‎ ‎[‎ ‎y_{n+1}=frac{alpha_n+y_n}{alpha_n+y_{n-k}},quad n=0,1,...‎, ‎]‎ ‎where $left{alpha_nright}_{ngeq0}$ is a bounded sequence of positive numbers‎, ‎$k$ is a positive integer and the initial values $y_{-k},...,y_0$ are positive real numbers‎. ‎We give sufficient conditions under which the unique equilibrium $bar{y}=1$ is globally asymptotically stable‎. ‎Furthermore‎, ‎we establish an oscillation result for positive solutions about the equilibrium point‎. ‎Our work generalizes and improves earlier results in the literature‎.

‎This paper proposes a direct four-step implicit hybrid block method for directly solving general fourth-order initial value problems of ordinary differential equations‎. ‎In deriving this method‎, ‎the approximate solution in the form of power series is interpolated at four points‎, ‎i.e $ x_n,,‎, ‎x_{n+1},,x_{n+2},,x_{n+3} $ while its forth derivative is collocated at all grid points‎, ‎i.e $ x_n‎, ‎,,x_{n+frac{1}{4}},,‎, ‎x_{n+1}‎ , ‎,,x_{n+2}‎, ‎,,x_{n+frac{5}{2}}‎, ‎,,x_{n+3}‎, ‎,,x_{n+frac{7}{2}} $ and $ x_{n+4} $ to produce the main continuous schemes‎. ‎In order to verify the applicability of the new method‎, ‎the properties of the new method such as local truncation error‎, ‎zero stability‎, ‎order and convergence are also established‎. ‎The performance of the newly developed method is then compared with the existing methods in terms of error by solving the same test problems‎. ‎The numerical results reveal that the proposed method produces better accuracy than several existing methods when solving the same initial value problems (IVPs) of second order ODEs‎.

In this paper‎, ‎we prove some fixed points properties and demiclosedness principle for mean nonexpansive mapping in uniformly convex hyperbolic spaces‎. ‎We further propose an iterative scheme for approximating a common fixed point of two mean nonexpansive mappings and establish some strong and $bigtriangleup$-convergence theorems for these mappings in uniformly convex hyperbolic spaces‎. ‎The results obtained in this paper extend and generalize corresponding results in uniformly convex Banach spaces‎, ‎CAT(0) spaces and other related results in literature.

‎Recently Hamed H Alsulami et al introduced the notion of‎ ‎($alpha$-$psi$)-rational type contractive mappings‎. ‎They have been‎ ‎establish some fixed point theorems for the mappings in complete‎ ‎generalized metric spaces‎. ‎In this paper‎, ‎we introduce the notion‎ ‎of some fixed points theorems for $alpha_{*}$-$psi$-common‎ ‎rational type mappings on generalized metric spaces with application‎ ‎to fractional integral equations and give a common fixed point‎ ‎result about fixed points of the‎ ‎set-valued mappings‎.

‎We are aimed to develop a fast and direct algorithm to solve linear‎ complementarity problems (LCP's) arising from option pricing problems‎. We discretize the free boundary problem of American options in temporal direction and obtain a sequence of linear complementarity problems (LCP's) in the finite dimensional Euclidian space $mathbb{R}^m$‎. ‎We develop a fast and direct algorithm based on the active set strategy to solve the LCP's‎. The active set strategy in general needs $O(2^m m^3)$ operations to solve $m$ dimensional LCP's‎. ‎Using Thomas algorithm‎, ‎we develop an algorithm with order of complexity $O(m)$ which can extremely speed up the computations‎.

‎In this paper we studying some properties of starlike function of order $lambda$ which satisfy in the condition‎ ‎$$Re(frac{zf^{'}(z)}{f(z)}+alphafrac{z^{2}f^{''}(z)}{f(z)})<1-lambda+alpha$$‎ ‎\for all $zin U={z:|z|<1}$‎, ‎where $f(z)=1+sum_{k=1}^infty a_{k}z^{k}$ is analytic in $U$‎, ‎$0leqslantalpha<2$ and $0leqslantlambda<1$‎. ‎Our results extend previos results given by Aghalary et al.‎ ‎(2009) and Wang et al.(2014).

‎In this article‎, ‎we introduce the notion of $(alpha,beta)$-generalized Meir-Keeler condensing operator in a‎ ‎Banach space‎, ‎a characterization using strictly L-functions and provide an extension of Darbo's fixed point theorem associated with measures‎ of noncompactness‎. ‎Then‎, ‎we establish some results on the existence of coupled fixed points for a‎ ‎class of condensing operators in Banach spaces‎. ‎As an application‎, ‎we study the‎ ‎problem of existence of entire solutions for a general system of nonlinear integral-differential equations in a Sobolev space‎. ‎Further‎, an example is presented to verify the effectiveness and applicability of our main results‎.

The main goal of this work, obtaining a family of Steffensen-type iterative methods adaptive with memory for solving nonlinear equations, which uses three self-accelerating parameters. For this aim, we present a new scheme to construct the self-accelerating parameters and obtain a family of Steffensen-type iterative methods with memory. The self-accelerating parameters have the properties of simple structure and easy calculation, which do not increase the computational cost of the iterative methods. The convergence order of the new iterative methods has increased from 4 to 8. Also, these methods possess very high computational efficiency. Another advantage of the new method is that they remove the severe condition $f'(x)$ in a neighborhood of the required root imposed on Newton's method. Numerical comparisons have made to show the performance of the proposed methods, as shown in the illustrative examples.‎

‎In this paper‎, ‎Avery-Henderson (Double) fixed point theorem and Ren fixed point theorem are used to investigate the existence of positive solutions for fractional-order nonlinear boundary value problems on infinite interval‎. ‎As applications‎, ‎some examples are given to illustrate the main results‎.

‎We investigate the existence and uniqueness of solutions for multi-point nonlocal boundary value problems of higher-order nonlinear fractional differential equations by using some well known fixed point theorems‎.

‎In this paper the implementation of parallel algorithm of alternating direction implicit (ADI) method has been considered‎. ‎ADI parallel algorithm is used to solve a multiphase multicomponent fluid flow problem in porous media‎. ‎There are various technologies for implementing parallel algorithms on the CPU and GPU for solving hydrodynamic problems‎. ‎In this paper GPU-based (graphic processor unit) algorithm was used‎. ‎To implement the GPU-based parallel ADI method‎, ‎CUDA and OpenCL were used‎. ‎ADI is an iterative method used to solve matrix equations‎. ‎To solve the tridiagonal system of equations in ADI method‎, ‎the parallel version of cyclic reduction (CR) method was implemented‎. ‎The cyclic reduction is a method for solving linear equations by repeatedly splitting a problem as a Thomas method‎. ‎To implement of a sequential algorithm for solving the oil recovery problem‎, ‎the implicit Thomas method was used‎. ‎Thomas method or tridiagonal matrix algorithm is used to solve tridiagonal systems of equations‎. ‎To test parallel algorithms personal computer installed Nvidia RTX 2080 graphic card with 8 GB of video memory was used‎. ‎The computing results of parallel algorithms using CUDA and OpenCL were compared and analyzed‎. ‎The main purpose of this research work is a comparative analysis of the parallel algorithm computing results on different technologies‎, ‎in order to show the advantages and disadvantages each of CUDA and OpenCL for solving oil recovery problems‎.

‎In this paper‎, ‎an inverse problem of determining an unknown reaction coefficient in a one-dimensional time-fractional reaction-diffusion equation is considered‎. ‎This inverse problem is generally ill-posed‎. ‎For this reason‎, ‎the mollification regularization technique with the generalized cross-validation criteria will be employed to find an equivalent stable problem‎. ‎Afterward‎, ‎a finite difference marching scheme is introduced to solve this regularized problem‎. ‎The stability and convergence of the numerical solution are investigated‎. ‎In the end‎, ‎some numerical examples are presented to verify the ability and effectiveness of the proposed algorithm‎.

‎In this paper‎, ‎B-spline collocation method is developed for‎ the solution of one-dimensional hyperbolic telegraph equation‎. ‎The‎ convergence of the method is proved‎. ‎Also the method is applied on‎ some test examples and the numerical results have been compared‎ with the analytical solutions‎. ‎The $L_infty$,$L_2$ and Root-Mean-Square‎ errors (RMS) in the solutions show the efficiency of the method‎ ‎computationally‎.

‎In this paper‎, ‎locally topologically transitive (or J-class) $C_0$-semigroups of operators on Banach spaces are studied‎. ‎Some similarity and differences of locally transitivity and hypercyclicity of $C_0$-semigroups are investigated‎. ‎Next the Kato's limit of a sequence of $C_0$-semigroups are considered and their locally transitivity relations are studied‎.

‎In this paper‎, ‎we develop the existence theory for some boundary‎ value problems of nonlinear $nth$-order ordinary differential‎ ‎equations supplemented with nonlocal Stieltjes boundary‎ conditions‎. ‎Our results are based on some standard theorems of‎ ‎fixed point theory and are well illustrated with the aid of‎ ‎examples‎.

Dams are always considered as infrastructure structures and have vital value. An earthen dam is a body consisting of discontinuous soil particles of various sizes that need to be placed in front of a stream of water to store it. As water is stored behind the dam and its surface area increases, the potential energy of the water particles increases and due to its porous nature, it begins to move in it. Today, the main problem that has attracted the attention of engineers is the issue of seepage. So that the presence of seepage in earthen dams is inevitable. The aim of the present study was to investigate the different positions of the sealing wall and to select the best angle, length, number and distance, as well as to select the appropriate length for horizontal drainage Due to the geotechnical conditions, it is against the phenomenon of rug and lifting force. GeoStudio software is a collection of soil mechanics software based on finite element method through which various modellings and analyzes can be examined. This software includes various models such as SEEP / W which is used for flow analysis and seepage. In the present study, the SEEP / W model of this software package has been used. The SEEP / W model is based on the Darcy relation, which expresses the passage of water flow through the soil in both saturated and unsaturated states. The results showed that for the sealing wall located above the core, an angle of 20 degrees and for the sealing wall located downstream of the core, an angle of 100 degrees are suitable. Also, the optimal length of the sealing wall is 24 meters and its optimal number is 2. Increasing the distance between the two vertical sealing walls has increased the lifting pressure and reduced the maximum outlet gradient. Increasing the horizontal drainage length reduced the maximum output gradient, while having little effect on the uplift pressure.

‎The main focus of this paper is to examine the effects of Gaussian white noise and Gaussian colored noise perturbations on the voltage of RC and RLC electrical circuits‎. ‎For this purpose‎, ‎the input voltage is assumed to be corrupted by the white noise and the charge is observed at discrete time points‎. ‎The deterministic models will be transferred to stochastic differential equations and these models will be solved analytically using Ito's lemma‎. ‎Random colored noise excitations‎, ‎more close to real environmental excitations‎, ‎so Gaussian colored noise is considered in these electrical circuits‎. ‎Scince there is not always a closed form analytical solution for stochastic differential equations‎, ‎then these models will be solved numerically based on the Euler‎- ‎maruyama scheme‎. ‎The parameter estimation for these stochastic models is investigated using the least square estimator when the parameters are missing data that it is a concern in electrical engeineering‎. ‎Finally‎, ‎some numerical simulations via Matlab programming are carried out in order to show the efficiency and accuracy of the present work‎.

‎Continuous stirred tank reactor (CSTR) is an important and constructive part in various chemical and process industries and therefore it is necessary to control the process in optimal temperature and concentration conditions. Because of the nonlinear nature and limits of the control input‎, ‎solving this problem is very difficult. To achieve a sub-optimal control policy for chemical processes‎, ‎we focused on a new construction model‎.  Then‎, ‎a two-phase algorithm‎, ‎denoted as modified sequential general variable neighborhood search (MSGVNS) algorithm based on three local searches that use efficient neighborhood interchange has been employed to solve CSTR problems numerically. The results of the proposed method show that its convergence to the exact solution is achieved by the accuracy comparable to other numerical algorithms in few times‎.

‎The combination of generalization Type-I hybrid censoring and generalization Type-II hybrid censoring schemes create a new censoring called a unified hybrid censoring scheme‎. ‎Therefore‎, ‎in this study‎, ‎the E-Bayesian estimation of parameters of the inverse Weibull distribution is obtained under the unified hybrid censoring scheme‎, ‎and the efficiency of the proposed method was compared with the Bayesian estimator using Monte Carlo simulation and a real data set‎.

‎The arrow domination is introduced in this paper with its inverse as a new type of domination‎. Let $G$ be a finite graph‎, ‎undirected‎, ‎simple and has no isolated vertex‎, ‎a set $D$ of $V(G)$ is said an arrow dominating set if $|N(w)cap (V-D)|=i$ and $|N(w)cap D|geq j$ for every $w in D$ such that $i$ and $j$ are two non-equal positive integers‎. ‎The arrow domination number $gamma_{ar}(G)$ is the minimum cardinality over all arrow dominating sets in $G$‎. ‎Essential properties and bounds of arrow domination and its inverse when $i=1$ and $j=2$ are proved‎. ‎Then‎, ‎arrow domination number is discussed for several standard graphs and other graphs that formed by join and corona operations‎.

‎This paper deals with existence and local attractivity of solution of a quadratic fractional integral equation in two independent variables‎. ‎The solution space has been considered to be the Banach space of all bounded continuous functions defined on an unbounded interval‎. ‎The fundamental tool used for the purpose is the notion of noncompactness and the celebrated Schauder fixed point principle‎. ‎Finally an example has been provided at the end in support of the result‎.

Two sample prediction is considered for a one-parameter exponential distribution‎. ‎In practical experiments using sampling methods based on different schemes‎ ‎is crucial‎. This paper addresses the problem of Bayesian prediction of record values from a future sequence‎, ‎based on an upper record ranked set sampling scheme‎. First‎, ‎under an upper record ranked set sample (RRSS) and different values of hyperparameters‎, ‎point predictions have been studied with respect to both symmetric and asymmetric loss functions‎. ‎These predictors are compared in the sense of their mean squared prediction errors‎. ‎Next‎, we have derived two prediction intervals for future record values‎. ‎Prediction intervals are compared in terms of coverage probability and expected length‎. ‎Finally‎, a simulation study is performed to compare the performances of the predictors‎. ‎The real data set is also analyzed for an illustration of the findings.‎

‎We use $Phi$-reflexive property on some geometrical structures(Fr"{o}licher spaces‎, ‎Sikorski spaces and diffeological spaces) to prove that some results on $(X,Upsilon)$-structures‎. ‎Finally‎, ‎we introduce $mathcal{P}$-tangent bundles‎, ‎$mathcal{F}$-tangent bundles and obtain a relation between these bundles and $Phi$-reflexive property‎.

‎In this paper‎, ‎we determine the different intervals of a positive parameters $lambda$‎, ‎for which we prove the existence and non existence of a non trivial solutions for the discrete problem (1.1)‎. ‎Our technical approach is based on the variational principle and the critical point theory‎.

‎In this paper‎, ‎using fixed point methods‎, ‎we prove the fuzzy orthogonally $*$-$n$-derivation on orthogonally fuzzy $C^*$-algebra for the functional equation‎‎begin{align*}‎‎begin{split}‎‎f(frac{mu x+mu y}{2}+mu w)+f(frac{mu x+mu w}{2}+mu y)+f(frac{mu y+mu w}{2}+mu x)‎‎=2mu f(x)-2mu f(y)-2mu f(w)‎.‎end{split}‎‎end{align*}‎

‎The main aim of this research article is to present the generalized $k$-fractional conformable integrals and an improved version of Gr$ddot{u}$ss integral inequality via the fractional conformable integral in status of a new parameter $k>0$‎. ‎Here for establishing Gr$ddot{u}$ss inequality in fractional calculus the classical method of proof has been adopted also related results with Gr$ddot{u}$ss inequality have been discussed‎. ‎This work contributes in the current research by providing mathematical results along with their verifications‎.

‎The inverse problem considered in this paper is devoted to reconstruction of the unknown source term in parabolic equation from additional information which is given by measurements at final time‎. ‎The cost functional is introduced and existence of the minimizer for this functional is established‎. ‎The numerical algorithm to solve the inverse problem is based on the Ritz-Galerkin method with shifted Legendre polynomials as basis functions‎. ‎Finally‎, ‎some numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for test example‎.

‎In the present paper‎, ‎we study a new subclass $mathcal{M}_p(alpha,beta)$ of $p$--valent functions and obtain some inequalities concerning the coefficients for the desired class‎. ‎Also‎, ‎by using the Hadamard product‎, ‎we define a new general operator and find a condition such that it belongs to the class $mathcal{M}_p(alpha,beta)$‎.

‎The system of double equations with three unknowns given by $d+ay+bx+cx^2=z^2‎ , ‎y+z=x^2$ is analysed for its infinitely many non-zero distinct integer solutions‎. ‎Different sets of integer solutions have been presented‎. ‎A few interesting relations among the solutions are given‎.

‎We propose to investigate the solutions of system of functional-integral‎ ‎equations in the setting of measure of noncompactness on real-valued bounded and continuous Banach space‎. To achieve this‎, ‎we first establish some new Darbo type fixed and coupled fixed point results for‎ $mu$-set $(omega,vartheta)$-contraction operator‎ ‎using arbitrary measure of noncompactness in Banach spaces‎. An example is given in support for the solutions of a pair of system of functional-integral‎ equations‎.

‎In this paper‎, ‎we give sufficient conditions for the existence of solutions‎ of a system of Volterra-type integral inclusion equations using new sort of‎ multi-valued contractions‎, ‎named as generalized multi-valued $alpha _{ast‎} ‎$-$eta _{ast }$-$theta $-contractions defined on $alpha $-complete‎ ‎b-metric spaces‎. ‎We give its relevance to fixed point results‎. ‎We set up an‎ ‎example to elucidate our main results‎.

‎In this paper‎, ‎we consider the class of generalized $Phi$-strongly monotone mappings and the methods of approximating a solution of equations of Hammerstein type‎. ‎Auxiliary mapping is defined for nonlinear integral equations of Hammerstein type‎. ‎The auxiliary mapping is the composition of bounded generalized $Phi$-strongly monotone mappings which satisfy the range condition‎. ‎Suitable conditions are imposed to obtain the boundedness and to show that the auxiliary mapping is a generalized $Phi$-strongly which satisfies the range condition‎. ‎A sequence is constructed and it is shown that it converges strongly to a solution of equations of Hammerstein type‎. ‎The results in this paper improve and extend some recent corresponding results on the approximation of a solution of equations of Hammerstein type‎.

‎In this paper, a  predator$-$prey model  with logistic growth rate in the prey population was proposed.  It included an SIS infection in the prey and predator population.  The stability of the positive equilibrium point, the existence of Hopf and transcortical  bifurcation with parameter $a$ were investigated, where $a$ was regarded as  predation rate. It was found that when the parameter $a$ passed through a critical value,  stability changed and Hopf bifurcation occurred.  Biologically, the population  is positive and bounded. In the present article,  it was also shown that the model was bounded and that it had the positive solution.  Moreover, the current researchers came to the conclusion that although  the disease was present in the system, none of the species would be extinct. In other words, the system was persistent. Important thresholds, $R_{0}, R_{1}$ and $R_{2}$, were identified in the study. This theoretical study indicated that under certain conditions of $R_{0}, R_{1}$ and $R_{2}$,  the disease remained in the system or disappeared.

‎In the present paper‎, ‎we introduce the recurrence relations of Vieta‎ ‎Fibonacci‎, ‎Vieta Lucas‎, ‎Vieta Pell and Vieta Pell Lucas polynomials‎. ‎We‎ obtain the generating functions of these polynomials‎, ‎then we give the new‎ ‎generating functions of the products of these polynomials and the products‎ ‎of these polynomials with Gaussian numbers and polynomials‎. ‎These results‎ ‎are based on the relation between Vieta polynomials and Chebyshev‎ ‎polynomials of first and second kinds‎.

‎The objective of the classical version of the minisum circle location problem is finding a circle $C$ in the plane such that the sum of the weighted distances from the circumference of $C$ to a set of given points is minimized‎, ‎where every point has a positive weight‎. ‎In this paper‎, ‎we investigate the semi-obnoxious case‎, ‎where every existing facility has either a positive or negative weight‎. ‎The distances are measured by the Euclidean norm‎. ‎Therefore‎, ‎the problem has a nonlinear objective function and global nonlinear optimization methods are required to solve this problem‎. ‎Some properties of the semi-obnoxious minisum circle location problem with Euclidean norm are discussed‎. ‎Then a cuckoo optimization algorithm is presented for finding the solution of this problem‎.

‎In this paper‎, ‎we establish the existence of at least three weak solutions for some one-dimensional $2n$-th-order equations in a bounded domain‎. ‎A particular case and a concrete example are then presented‎.

Over the last three decades, artificial intelligence has attracted lots of attentions in medical diagnosis tasks. However, few studies have been presented to assist urologists to diagnose bladder cancer in spite of its high prevalence worldwide. In this paper, a new computer aided diagnosis system is proposed to classify four types of cystoscopic images including malignant masses, benign masses, blood in urine, and normal. The proposed classifier is an ensemble of a well-known type of convolutional neural networks (CNNs) called VGG-Net. To combine the VGG-Nets, bootstrap aggregating approach is used. The proposed ensemble classifier was evaluated on a dataset of 720 images. Based on the experiments, the presented method achieved an accuracy of 63% which outperforms base VGG-Nets and other competing methods.

‎Outlier detection is a technique for recognizing samples out of the main population within a data set‎. ‎Outliers have negative impacts on classification‎. ‎The recognized outliers are deleted to improve the classification power generally‎. ‎This paper proposes a method for outlier detection in test samples besides a supervised training set selection‎. ‎Training set selection is done based on the intersection of three well known similarity measures namely‎, ‎jacquard‎, ‎cosine‎, ‎and dice‎. ‎Each test sample is evaluated against the selected training set for possible outlier detection‎. ‎The selected training set is used for a two-stage classification‎. ‎The accuracy of classifiers are increased after outlier deletion‎. ‎The majority voting function is used for further improvement of classifiers‎.

The aim of this paper is to investigate some new types of neutrosophic continuous mappings like, neutrosophic α ∗−continuous mapping (Nα∗ − CM), neutrosophic irresolute α ∗−continuous mapping (NIα∗ − CM), and neutrosophic strongly α ∗−continuous mapping (NSα∗ − CM) are given and some of their properties are studied. Moreover, new kind of neutrosophic contra continuous mappings is investigated in this work, it is called neutrosophic contra α ∗−continuous mapping (NCα∗ − CM).

he aim of this research is to initiate a new concept of domination in fuzzy graphs which is called a fuzzy co-even domination number denoted by $gamma_{f c o}(G) .$ We will touch only a few aspects of the theory to of this definition. Some properties and boundaries of this definition are introduced. The fuzzy co-even domination number of fuzzy certain graphs as fuzzy complete, fuzzy complete bipartite, fuzzy star, fuzzy cycle, fuzzy null, fuzzy path, and fuzzy star are determined. Additionally, this number is computed for the complement of mentioned above fuzzy certain graphs. Finally, this number is also determined for the join to mentioned above fuzzy certain graphs with itself.

‎In this paper‎, ‎some fixed point theorems for non-expansive mappings in partially ordered spherically complete ultrametric spaces are proved‎. ‎In addition‎, ‎we investigate the existence of fixed points for nonexpansive mappings in partially ordered non-Archimedean normed spaces‎. ‎Finally‎, ‎we give some examples to discuss the assumptions and support of these theorems.‎

In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $T$ be a multivalued mappings on $X.$ Among other things, we obtain a fixed point of the mapping $T$ in the metric space $X$ endowed with a graph $G$ such that the set of vertices of $G,$ $V(G)=X$ and the set of edges of $G,$ $E(G)subseteq Xtimes X.$

In this paper, we establish complex valued $G_b$-metric spaces and introduced the notion of $G_b$-Banach Contraction, $G_b$-Kannan mapping and prove fixed point theorems in the such spaces.

The present paper provides a new method for numerical solution of nonlinear boundary value problems. This method is a combination of group preserving scheme (GPS) and a shooting--like technique which takes advantage of two powerful methods for solving nonlinear boundary value problems. This method is very effective to search unknown initial conditions. To demonstrate the computational efficiency, the mentioned method is implemented for some nonlinear exactly solvable differential equations including strongly nonlinear Bratu equation, nonlinear reaction--diffusion equation and one singular nonlinear boundary value problem. It is also applied successfully on two nonlinear three--point boundary value problems and a third--order nonlinear boundary value problem which the exact solutions of this problems are unknown. The examples show the power of method to search for unique solution or multiple solutions of nonlinear boundary value problems with high computational speed and high accuracy. In the test problem 5 a new branch of solutions is found which shows the power of the method to search for multiple solutions and indicates that the method is successful in cases where purely analytic methods are not.

In this study, we present the new Hermite-Hadamard type inequality for functions which are $h$-convex on fractal set $mathbb{R}^{alpha }$ $(0<alpha leq 1)$ of real line numbers. Then we provide the special cases of the result using different type of convex mappings.

In this paper, we first give a separation theorem for a closed star-shaped set at the origin and a point outside it in terms of separation by an upper semi-continuous and super-linear function, and also, we introduce a $nu$</span>-star-shaped-conjugation. By using this facts, we present characterizations of the set containment with infinite star-shaped constraints defined by weak inequalities. Next, we give characterizations of the set containment with infinite evenly radiant constraints defined by strict or weak inequalities. Finally, we give a characterization of the set containment with an upper semi-continuous and radiant constraint, in a reverse star-shaped set, defined by a co-star-shaped constraint. These results have many applications in Mathematical Economics, in particular, in Utility Theory.

In this paper, we investigate solutions of nonlinear fractional differential equations by using Natural homotopy perturbation method (NHPM). This method is coupled by the Natural transform (NT) and homotopy perturbation method (HPM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the presented method.

Reaction automata direct graph (RADG) is a new technique that uses the automata direct graph method to represent a certain design for encryption and decryption. Jump states are available in the RADG design that enables the encipher to generate different ciphertexts each time from the same plaintext and wherein not a single ciphertext is related to a certain plaintext. This study created a matrix representation for RADG designs that allows the calculation of the number of cases ($F_{Q}$)mathematically possible for any design of the set $Q$. $F_{Q}$ is an important part of the function $mathrm{F}(mathrm{n}, mathrm{m}, lambda)$ that calculates the total number of cases of a certain design for the values $Q, R, sum, psi, J$ and $T$. This paper produces a mathematical equation to calculate $F_{Q}$.

This paper introduces a new proposed algorithm of numerical integration evaluation regarded as optimization problem solution. The new method is characterized to have superiority features such as attractive, accurate and rapid. An improvement of polynomial regression has been done by selecting nearest neighbors points being searched around of the values of regression coefficients which calculated by using least squares method. Furthermore, Trapezoidal and Simpson methods were considered as traditional methods in numerical integration. In this regard, comparison has been done among all four methods used in simulation application via MATLAB program that have been performed to achieve the desired numerical results for the four methods. As conclusion, the proposed algorithm approved its superiority.

We present a model of the fluid flow between elastic walls simulating arteries actively interacting with the blood. The lubrication theory for the flow is coupled with the pressure and shear stress from the walls. The resulting nonlinear partial differential equation describes the displacement of the walls as a function of the distance along the flow and time.

By using the subordination relation $"prec"$, we introduce an interesting subclass of analytic functions as follows: begin{equation*}
mathcal{S}^*_{alpha}:=left{fin mathcal{A}:frac{zf'(z)}{f(z)}prec frac{1}{(1-z)^alpha}, |z|<1right},
end{equation*}
where $0<alphaleq1$ and $mathcal{A}$ denotes the class of analytic and normalized functions in the unit disk $|z|<1$. In the present paper, by the class $mathcal{S}^*_{alpha}$ and by the Nunokawa lemma we generalize a famous result connected to starlike functions of order $1/2$. Also, coefficients inequality and logarithmic coefficients inequality for functions of the class $mathcal{S}^*_{alpha}$ are obtained.

The aim of this paper is to construct a complete metric space of fuzzy valued image functions and to define a fractal transform operator T. Contraction of T is guarantees the existence of its fixed point. A fuzzy point is considered for this purpose as a crisp point and approached through classical method on proving the completeness of the space.

A new approach is proposed for classifying the problems of determining the maximum common fragments $(M C F)$ for two connected structures included in the $T$-digraph, based on the type of the maximum common fragment. A tree of classification the problems of determining the maximum common fragments $(M C F)$ for two structures $t_{i} G, t_{j} Gleft(M C Fleft(t_{i} G, t_{j} Gright)right)$ included in the $T$-digraph is proposed. Examples are given for a digraph $t G$ with three types of its fragments (parts), and for five connectivity types of digraphs. The formulation of six basic problems of determining the maximum common fragments $ (MCF) $ for two connected structures included in the $T$-digraph is given. A classification is proposed for an isomorphic embedding of a digraph into another.

Lie’s theory of symmetry groups plays an important role in analyzing and solving differential equations; for instance, by decreasing the order of equation. Moreover, there are some analytic methods to find the infinitesimal generators that span the Lie algebra of symmetries. In this paper, we first converted the problem of finding infinitesimal generators in to the problem of solving a system of polynomial equations in the context of computational algebraic geometry. Then, we used Gröbner basis a novel computational tool to solve this problem. As far as we know, when a differential equation contains some parameters, there is no linear algebraic algorithm up to our knowledge to deal with these parameters; so, we must apply the algorithms, which are based on Gröbner basis.

Using the concept of extended Wardowski-Mizoguchi-Takahashi contractions, we investigate the existence of solutions for three type of nonlinear fractional differential equations. To patronage our main results, some examples of nonlinear fractional differential equations are given.

In this paper, we prove a new common fixed point in a general topological space with a $tau-$distance. Then we deduce two common fixed point theorems for two new classes of contractive selfmappings in complete bounded metric spaces. Moreover, an application to a system of differential equations is given.

In this paper a new kind of graph on a commutative semiring is introduced and investigated. The maximal ideal graph of S, denoted by MG(S), is a graph with all nontrivial ideals of S as vertices and two distinct vertices I and J are adjacent if and only if I + J is a maximal ideal of S. In this article, some interrelation between the graph theoretic properties of this graph and some algebraic properties of semirings are studied. We investigated the basic properties of the maximal ideal graph such as diameter, girth, clique number, cut vertex, planar property.

In the setting of non-reflexive spaces (Grothendieck Banach spaces), we establish (1) ran (A+B)=ran A+ran B (2) int (ran (A+B))=int(ran A+ran B). with the assumption that A is a maximal monotone operator and B is a single-valued maximal monotone operator such that A+B is ultramaximally monotone. Conditions (1) and (2) are known as Br$acute{e}$zis-Haraux conditions.

This paper introduces and developed a new lifetime distribution known as inverse exponential Rayleigh distribution (IERD). The new two-scale parameters generalized distribution was studies with its distribution and density functions, besides that the basic properties such as survival, hazard, cumulative hazard, quantile function, skewness, and Kurtosis functions were established and derived. To estimate the model parameters, maximum likelihood, and rank set sampling estimation methods were applied with real-life data.

In this article, we first presented a new integral identity concerning differentiable mappings defined on m-invex set. By using the notion of generalized relative semi-$(r; m, p, q, h_1, h_2)$-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Ostrowski type conformable fractional integral inequalities are established. It is pointed out that some new special cases can be deduced from main results of the article.

In this paper, we introduce the concept of $(psi, phi)$-Suzuki and $(psi, phi)$-Jungck-Suzuki contraction type mappings and we establish the existence, uniqueness and coincidence results for $(psi, phi)$-Suzuki and $(psi, phi)$-Jungck-Suzuki contraction mappings in the frame work of complete metric spaces. As an application, we apply our result to find the existence and uniqueness of solutions of a differential equation.

In this paper, authors discover two interesting identities regarding Gauss--Jacobi and trapezium type integral inequalities. By using the first lemma as an auxiliary result, some new bounds with respect to Gauss--Jacobi type integral inequalities for a new class of functions called strongly $(h_{1},h_{2})$--preinvex of order $sigma>0$ with modulus $mu>0$ via general fractional integrals are established. Also, using the second lemma, some new estimates with respect to trapezium type integral inequalities for strongly $(h_{1},h_{2})$--preinvex functions of order $sigma>0$ with modulus $mu>0$ via general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from main results. Some applications to special means for different real numbers and new approximation error estimates for the trapezoidal are provided as well. These results give us the generalizations of some previous known results. The ideas and techniques of this paper may stimulate further research in the fascinating field of inequalities.

Using the techniques of the differential subordination and superordination, we derive certain subordination and superordination properties of multivalent functions associated with the Dziok-Srivastava operator.

There are few papers deals with stability of the inverse domination number in graphs by adding new edge to the graph or removing edge or vertex. Before this type of study, we need to know the stability of the domination number, then check the stability of the inverse domination. In this paper, the inverse pitchfork domination number γ −1 pf (G) is studied to be changing or not after adding or removing edge or removing vertex. Some conditions are putted on the graph to be affected or not with several results and examples.

Different estimation procedures for the probability density and cumulative distribution functions
of the generalized inverted Weibull distribution are discussed. For this purpose, the parametric and non-parametric estimation approaches as maximum likelihood, uniformly minimum variance unbiased, percentile, least squares and weighted least squares estimators are considered and compared. The expectations and mean square error of the maximum likelihood and uniformly minimum variance unbiased estimation are provided in the closed-form whereas, for non-parametric estimation methods (percentile, least squares and weighted least squares), the expectations and mean square error are computed via the simulation data. The Monte Carlo simulations are provided to assess the performances of the proposed estimation methods. Finally, the analysis of the real data set has been presented for illustrative purposes.

The main purpose of present article is proposed an effective method for robust fitting penalized regression splines models. According to such a context a comparative analysis with two common robust techniques, M-type estimator, S-type estimator, and non-robust least squares (LS) for penalized regression splines (PRS) has been implemented. Because the penalized regression splines are recently a common approach to smoothing noisy data for its simplicity, efficiency, and significantly reducing disturbance of outliers and its flexibility in monitoring nonlinear data trends. In many cases, it is difficult to determine the most suitable form and a way of designing a data is needed when faced with many smoothing problems. The executing aspects of fitting precision and robustness of the four estimators have a thorough evaluation of their performance on R codes. A comparative analysis demonstrates that the proposed method can resist the noise effect in both simulated and real data examples compared to other robust estimators with different combinations of contamination. These findings are used as guidance for finding a specific method to pulsing smoothing noisy data

In this paper we study the notion of Gerghaty type contractive mapping via simulation function along with $mathcal{C}$-class functions and prove the existence of several fixed point results in ordinary and partially ordered metric spaces. An example is given to show the validity of our results given herein. Moreover, existence of solution of two-point boundary value second order nonlinear differential equation is obtain.

This paper proposes a nonlinear programming model for a scheduling problem in the supply chain. Due to the nonlinear structure of the developed model and its NP-hard structure, a lower bound is developed. Four lemmas and a theorem are presented and proved to determine the lower bound. The proposed problem is inspired from a three stage supply chain commonly used in various industries.

In this study, the dynamical behavior of the four-dimensional (4D) hyperchaotic system is analyzed. Its chaotic dynamical behaviors and basic dynamical properties are presented by Lyapunov exponents, stability analysis, and Kaplan-Yorke dimension. Then, the control of 4D hyperchaotic system is implemented by using passive control. The global asymptotic stability of the system is guaranteed by using Lyapunov function. Simulation results are shown to validate all theoretical analysis and demonstrate the effectiveness of the proposed control method. By applying the passive controllers, the system under chaotic behavior converges to the equilibrium point at origin asymptotically.

We generalize the notion of the anti-Daugavet property (a-DP) to the anti-N-order polynomial Daugavet property (a-NPDP) for Banach spaces by identifying a good spectrum of a polynomial and prove that locally uniformly alternatively convex or smooth Banach spaces have the a-mDP for rank-1 polynomials. We then prove that locally uniformly convex Banach spaces have the a-NPDP for compact polynomials if and only if their norms are eigenvalues, and uniformly convex Banach spaces have the a-NPDP for continuous polynomials if and only if their norms belong to the approximate spectra.

In this work, some new connotations of continuous mappings such as $alpha^{*}$ - continuous mapping $left(alpha^{*}-C Mright),$ irresolute $alpha^{*}-$mapping $left(I alpha^{*}-C Mright),$ and strongly $alpha^{*}-$ continuous mapping $left(S alpha^{*}-C Mright)$ are studied and some of their characteristics are discussed. In other side, new some classes of contra continuous mappings are investigated in this work, they are called contra $alpha^{*}$ - continuous mapping $left(C alpha^{*}-C Mright)$.

The point of the current investigation is to research one of the extremely significant groups exceedingly associated with the classical group which is called the special unitary groups $SU_{2}(K)$ particularly of degree $2$. Let $K$ be a field of characteristic, not equal $2$, our principal objective that to depicting subgroups of $SU_{2}(K)$ over a field $K$ contains all elementary unitary transvections.

This paper deals with the solution of the unconstrained optimization problems on parallel computers using quasi-Newton methods. The algorithm is based on that parallelism can be exploited in function and derivative evaluation costs and linear algebra calculations in the standard sequential algorithm. Computational problem is reported for showing that the parallel algorithm is superior to the sequential one.

This paper presents an integrated three layer supply chain policy for multi-channel and multi-echelon consisting manufacturer, distributors and retailers as  supply chain members. The demand of retailers end is considered as linear function of  time and retail price. The average net profit function per unit  time is derived for each  supply chain member which are based on demand of retailer's  end. Since  holding cost of goods/inventory is expensive in developed areas, we have introduced a new concept  to share holding cost among distributors and retailers. We have  optimized lot size, retailing price and replenishment time interval for retailers. We have also optimized initial inventory level and wholesale price for distributors and manufacturer respectively. This  study is performed in two different  categories one is decentralized and other  is centralized scenario. The profit function of each supply  chain members has been derived and shown as a concave function with respect to decision variables. More over propositions and results are made to illustrate the proposed model and we have sensitive  analyzed it with numerical example.

We show in this paper that a mapping $f$ satisfies the following functional equation begin{eqnarray*} biguplus_{x_2,cdots,x_{d+1}}^{d}f(x_1) = 2^{d} sum_{i=1}^{d+1}f(x_i), end{eqnarray*} if and only if it is quadratic. In addition, we investigate generalized Hyers-Ulam stability problem for the equation, and thus obtain an asymptotic property of quadratic mappings as applications.

By introducing independent parameters and applying the weight coefficients, we use Hermite-Hadamard's inequality and give a more accurate Hardy-Hilbert's inequality in the whole plane with a best possible constant factor. Furthermore, the equivalent forms, a few particular cases and the operator expressions are considered.

In this study, we obtain exact traveling wave solutions of the conformable space-time fractional Sawada-Kotera-Ito, Lax and Kaup-Kupershmidt equations by using the extended tanh method. The obtained traveling wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Simulation of the obtained solutions are given at the end of the paper.

We consider the initial value problem for a class of nonlinear fractional neutral functional differential  equations with infinite delay involving the standard fractional derivative in the sense of Caputo. By using  a variety of tools of fractional calculus including the Banach contraction principle and the Schaefer fixed point theorem, the existence, uniqueness and continuous dependence results are obtained in the space of continuous functions.

An existence result of renormalized solutions for nonlinear parabolic Cauchy-Dirichlet problems whose model $$left{begin{array}{ll} displaystylefrac{partial b(x,u)}{partial t} -mbox{div}>mathcal{A}(x,t,u,nabla u)-mbox{div}> Phi(x,t,u)= f &mbox{ in }Omegatimes (0,T)\ b(x,u)(t=0)=b(x,u_0) & mbox{ in } Omega\ u=0 &mbox{ on } partialOmegatimes (0,T). end{array}right. $$ is given in the non reflexive Musielak spaces, where $b(x,cdot)$ is a strictly increasing $C^1$-function for every $xinOmega$ with $b(x,0)=0$, the lower order term $Phi$ is a non coercive Carath'{e}odory function satisfying only a natural growth condition described by the appropriate Musielak function $varphi$ and $f$ is an integrable data.

In this paper, we introduce and study a new class of soft sets, called soft $b^*$-closed and soft $b^*$-open sets. we study several characterizations and properties of these class of sets.

Accelerated failure time model sometimes symbolized as AFT model, is an important  regression model in survival analysis. In this article, we applied AFT model to the data of lung cancer patient in order to identify the must important factors affecting the patient's survival time. The results showed a well performance for this model, as based on some statistical criteria, the factors  that are consistent with the opinion of specialists in in uencing survival time were identified, as the  factors (smoking, treatment, proliferation, location of residence) of the main factors aecting the life of a person with this disease.

In this paper, the concept of $etaxi$-monotonous operator is explored using KKM mapping. The  existence results and uniqueness de ned on its bounded and unbounded domains are discussed. Our ndings improve and develop some well-known solutions in literature.

This study aims to design a multi-period credit portfolio optimization model with a nonlinear multi-objective fuzzy mathematical modeling approach. In terms of data collection, this study is a descriptive-survey research and in terms of the nature and purpose of the research, it is an applied one. The statistical population of the research includes all facility files of the last 10 years as well as the statements of financial position of Ansar Bank branches affiliated with Sepah Bank, selected by census method. The risk criteria used in the models include Average Value at Risk (AVaR), Conditional Value at Risk (CVAR) and Semi-Entropy. First, having reviewed the research literature, the objectives and indices of the portfolio optimization issue were investigated based on the practical character of this issue and the main indices were selected. Then, each of the objectives and constraints were specified in a state of uncertainty and ambiguity, based on the principles of fuzzy credibility theory, for a state in which the expected rate of stock return is a triangular fuzzy number. Finally, three multi-objective fuzzy models were designed based on the selected criteria. Research models were implemented using MOPSO algorithm. The software used in conducting the research was MATLAB software. The results indicated that the CVAR model performed better than the other two models, i.e. AVAR and Semi-Entropy, in evaluating optimal portfolios.