مجله پژوهش های نوین در ریاضی
پیاپی 35 (فروردین و اردیبهشت 1401)

Investigating the mean ergodicity of composition operators on various Banach Spaces has always been of interest to mathematicians and many authors studied this topics intensively, in many different spaces, such as, the space of all holomorphic functions on unit disk, Hardy space and Bloch space. In this paper, for a self map of the unit disk, φ and λ∈ℂ, we consider weighted composition operator, (λ𝐶φ)𝑓=λ𝑓𝑜φ , for every 𝑓 in Bloch space and Little Bloch space and inquiry the conditions under which the weighted composition operator 𝜆𝐶𝜑, is mean ergodic or uniformly mean ergodic on the Bloch and Little Bloch Space. In fact, we will show, if |λ|>1,𝜆𝐶𝜑, cannot be power bounded, mean ergodic or uniformly mean ergodic, in contrast, if |λ|<1, 𝜆𝐶𝜑, is always power bounded, mean ergodic or uniformly mean ergodic. In the case, |λ|=1, we will see that it depends directly to the Denjoy-Wolff point of 𝜑.

In many applied research, the researcher does not have access to all the data for some reasons such as time and cost constraints. So, the statistical inference based on the available data is important. In this paper, estimation of unknown parameters of a generalized inverted exponential distribution is studied under generalized Type II progressive hybrid censoring. The maximum likelihood estimators and their existence and uniqueness are investigated. Based on the Bayesian approach, the estimators of the shape and scale parameters are derived under squared error loss function. Since closed - form expressions for the Bayes estimators cannot be obtained, we use Lindley’s approximation and important sampling procedure for obtaining them. Simulation study for comparing the different classical and Bayesian estimations is presented. Finally, two real data sets contain oblique impact of micro droplets onto surface in plasma spray coating process and repair time for a communication transmitter are analyzed for illustration purposes.

Data Envelopment Analysis (DEA) is a broad range of mathematical models for measuring the relative efficiency of a set of homogeneous decision units with similar inputs and outputs. Multiple models of data envelopment analysis render a set of weights for input and output variables of each decision unit to calculate the relative efficiency of those units based on them. The calculation of different weights for the same indices in a set of homogeneous decision units is not realistic. Therefore, the Common Set of Weights (CSW) method was used to solve this problem and the Bootstrap method was used to determine which common set of weights would minimize the number of efficient units. The rank of a unit can provide useful information to decision-makers on the optimal activities of decision units. The priority order of units defines the superiority of a unit in terms of efficiency and effectiveness over others. Calculating unit efficiency for data envelopment analysis models can be a good criterion for ranking one unit. However, the main problem arises when several efficient units all rank first. This study aimed at proposing a model for ranking efficient units using the Bootstrap method to determine the common set of weights in data envelopment analysis by finding a possible confidence interval for the weights using the Bootstrap method. This led to the estimation of a set of possible common weights for the data envelopment analysis. Efficient units were then identified and ranked based on these weights..

Recently, samet et al. introduced an interesting extension of the Banach contraction principle. In this paper, motivated by the main idea of Samet et al., we introduce the concept of α-admissible α-θ-generalized mappings in metric spaces and give and prove several theorems of the existence and uniqueness of a fixed point in complete metric spaces for such mappings. The results obtained in this study, generalize many of the results in this field, especially, the results presented by Jleli et al. and the work done by Geraghty. By presenting an example, we show that our results are real generalization of the previous results. Next, we get new results in ordered metric spaces and graphical metric spaces using the concept of α-admissible α-θ-generalized mappings. Finally, we present an application of our obtained results for the existence and uniqueness of the solution of nonlinear first-order ordinal differential equations and periodic boundary value problems.

Lie symmetry analysis provides an efficient method to get the analytical and exact solutions of the fractional differential equations. In this paper, we discuss Lie symmetry analysis for the time-fractional equal width wave equation with Riemann–Liouville derivative. This equation is used to describe the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes. By employing classical and nonclassical Lie symmetry analysis and some technical calculations, new infinitesimal generators are obtained. Then we reduce the fractional equal width wave equation to the ordinary fractional differential equation by changing the coordinates and find invariant solutions to this equation. By means of Ibragimov’s new conservation theorem and the generalization of the Noether operators, we construct the conservation laws for the equation. Also, we derive the adjoint equation and infinitesimal generator associated with Lie symmetries of the underlying equation and we reduce this equation to the ordinary fractional differential equation. In the reduced equations the derivative is in Erdelyi–Kober sense.

Ordered Banach spaces are very significant class of vector spaces which are studied widely in theory and applications of mathematics. On the other hand, an important theory in mathematical analysis is fixed point theory. This theory and its applications in ordered Banach spaces have been considered by many researchers. Lakshmikantham have proved some fixed point theorems in ordered Banach space X for a Fréchet differentiable automorphism on X. Mouhadjer and Benahmad obtained some generalizations of Lakshmikantham’s fixed point theorems. They introduced a monoton Newton-like method, by using Lakshmikantham’s fixed point theorems. Recently, a non-smooth version of Lakshmikantham’s theorem in finite dimentional ordered Banach spaces.has been obtained by authores. Also an application of the obtained results in the Coulomb friction problem has been presented. In this paper, we present a non-smooth version of Mouhadjer and Benahmad’s results. We prove some fixed point theorems for Lipschitzian mappings on finite Banach spaces which are not necessary Fréchet differentiable. Our main tool is Clarke generalized Jacobian

Given the importance of banking systems and the misuse of this platform for money laundering purposes, the urgent need for the implementation of anti-money laundering systems by governments and policy makers in economic affairs is important. Also, due to the growth of terrorism and organized fraud, and the passage of numerous laws against these cases, the need for these systems is increasing. On the other hand, the complexity of money laundering suspicious behaviors is such that no significant action can be taken to detect money laundering without intelligent and data-driven tools. An important and perhaps practical point in Iran is the proximity of these systems to anti-bribery, fraud, violation and inspection systems, which can be considered as an efficient tool for the bank's inspection unit. This paper presents an approach based on data analysis and processing. In this approach, using self-organizing maps, bank branches are clustered based on similar behaviors, then the process of labeling branches is performed using a linear index. In the next step, using the training of a multi-layer neural network, a model for identifying bank branches in which suspicious money laundering processes take place is introduced.

Gutman defined graph energy and then different types of energy were introduced. The energy of a graph G, is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix.In this paper we study energy and resolvent energy of the convex linear combinations A_α (G) of a simple undirected graph G defined byA_α (G)≔αD(G)+(1-α)A(G) for any real 0≤α≤1 . We show that the solvent energy of A_α (G) is increasing in α, as well as the energy of A_α (G) is increasing in α if α> 1/2. we give a few additional bounds on energy of A_α (G) in terms of the degrees of the vertices of graph G. For regular graph G, we present lower and upper bounds on the energy of A_α (G). We compute energy and resolvent energy of path P_n and cycle C_n . Finally, we calculate the energy and resolvent energy of A_α (G) for complete graphs K_n, complete bipartite graphs K_(a,b), and stars K_(1,n-1) (S_n).

The main concept in this paper is the notion of the J-Householder matrix and its main applications. From these cases are the achievement to QR-decomposition, where Q is a J-Orthogonal matrix and R is an upper triangular matrix and reduction to the Hessenberg form and the tridiagonal form, for J-symmetric matrices.The reduction problem to condensed forms of triangular, Hessenberg and tridiagonal is one of the important problem in the numerical linear algebra. It is thestructures of these condensed forms that are exploited in the solution of the reduced problem. For example, as we have seen in [2], [3],[7], [8], [6], [9] and [10], thesolution of the linear system Ax = b is usually obtained by first triangularizing thematrix A and then solving an equivalent triangular system. In [8], for reductionto a condensed form, the concept of J−unitary similarity is used, while in the restis used in the ordinary sense. In eigenvalue computations, the matrix A is transformed to a Hessenberg form befor applying the QR iterations. In [1], for reductionto a condensed form, the concept of J−unitary similarity is used. These condensedforms are Householder transformations and mybe J−Householder transformations.

The Kirchhoff equation(*) [rho frac{{{partial ^2}u}}{{partial {t^2}}} - left( {frac{{{P_0}}}{h} + frac{E}{{2L}}int_0^L {left| {frac{{partial u}}{{partial x}}} right|} dx} right)frac{{{partial ^2}u}}{{partial {x^2}}} = 0]extends the classical d'Alembert's wave equation by considering the effects of the changes in the length of the strings during the vibrations. The parameters in equation (*) have the following meanings: L is the length of the string, h is the area of cross-section, E is the Young modulus of the material, rho is the mass density and P_0 is the initial tension. In recent years, some applicable generalization of Kirchhoff equation have been proposed and studied in many papers. In this paper, we study the existence of positive weak solutions for new Kirchhoff type systems with multiple parameters. We will show under what conditions these systems have a positive weak solution for any positive parameters. Our approach in this paper is based on the sub- and supersolution method. approach in this paper is based on the sub- and supersolution method.

The current definition of the derivative makes the set of differentiable functions much smaller than the set of continuous functions, such that most of the real single variable functions are not differentiable and the surveying the rate of their growth is not possible with the available definition. In the present paper, using Caratheodory definition, we extend the set of differentiable functions by introducing a definition for generalized differentiation of a single variable function and its generalized derivative, in such a way that the validity of the basic theorems of this theory such as Rolle's theorem, Cauchy's mean value theorem, mean value theorem and Taylor's theorem would be hold. Finally we give some examples

Uncertainty is the obvious attribute of any activity in the real world, and performance analysis of units in terms of uncertainty is one of the most important concerns of managers and planners of companies. Various approaches to data envelopment analysis have been presented so far to provide a good tool for evaluating the efficiency of units in uncertain situations, including random, fuzzy and robust approaches. In a situation where the probability distribution function of random variables is known, stochastic approach is a precise solution for problem solving. Nevertheless, previous research in this field has focused on the transformation of a random problem into a definite problem. In this research, a method for modeling data envelopment analysis is presented using computer programming. In this method, random processes are simulated, and finally, the performance distribution function is presented instead of a definite number as the unit's efficiency. In this model, a new concept is presented as the probability of efficiency, which represents the probability that the unit will be located on the efficient boundary. The proposed method is empirically applied in a real case of selecting research and development projects.

In this paper, we first introduce the nearest and the farthest points in normed spaces, then introduce nonlinear semi inner product spaces, negative dual sets and sun sets. We make statements about these concepts. Define the concept of orthogonality of the nonlinear semi inner product and describe its properties. Finally, we bring the nearest and the farthest points in linear spaces. we introduce the nearest and the farthest points in normed spaces, then introduce nonlinear semi inner product spaces, negative dual sets and sun sets. We make statements about these concepts. Define the concept of orthogonality of the nonlinear semi inner product and describe its properties. Finally, we bring the nearest and the farthest points in linear spaces. we bring the nearest and the farthest points in linear spaces. we introduce the nearest and the farthest points in normed spaces, then introduce nonlinear semi inner product spaces, negative dual sets and sun sets. We make statements about these concepts. Define the concept of orthogonality of the nonlinear semi inner product and describe its properties. Finally, we bring the nearest and the farthest points in linear spaces.

The most geometric properties of inner product spaces like strict convexity and smoothness my fail to hold in a general normed linear spaces. Also, some main properties of the orthogonality in inner product spaces do not always carry over to generalized orthogonalities. Taking these into account different types of orthogonality relations provide a good frame for studying the geometric properties of normed linear spaces. In this paper, we give a characterization of inner product spaces using the notion of Hermite–Hadamard type of Carlsson’s orthogonality in normed linear spaces. First, we provide some more results about the existence property of this orthogonality. Next, we prove that Hermite-Hadamard type of Carlsson’s orthogonality is additive in a normed linear space X if and only if X is an inner product space. Our approach to prove this fact is using the relationship between Birkhoff-James orthogonality and the Gateaux differentiability of the norm of normed linear spaces.

Let G=(V, E) be a simple graph with vertex set V and edge set E. An outer-paired dominating set D of a graph G is a dominating set such that the subgraph induced by V\D has a perfect matching. The outer-paired domination number of G denoted by is the minimum cardinality of an outer-paired dominating set of G. Moreover, a total outer-paired dominating set D of a graph G is a total dominating set such that the subgraph induced by V\D has a perfect matching. The total outer-paired domination number of G denoted by is the minimum cardinality of a total outer-paired dominating set of G. In this paper, besides introducing such a notion for a graph, we study some fundamental properties of this invariant. Furthermore, we present some bounds in terms of the order, the size, the girth of a graph and etc. Finally, the well-known Nordhaus-Gaddum inequality is obtained for regular graphs.