فهرست مطالب

International Journal Of Nonlinear Analysis And Applications
Volume:8 Issue: 2, Winter - Spring 2017

  • تاریخ انتشار: 1396/10/30
  • تعداد عناوین: 30
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  • Hemant Nashine *, Zoran Kadelburg Pages 1-8
    In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend some results existing in the literature.
    Keywords: common best proximity point, optimal approximate solution, proximally commuting mappings
  • Ali Arefmanesh, Mahmoud Abbaszadeh* Pages 9-22
    By using the finite element p-Version in convection-diffusion problems, we can attain to a stabilized and accurate results. Furthermore, the fundamental of the finite element p-Version is augmentation degrees of freedom. Based on the fact that the finite element and the meshless methods have similar concept, it is obvious that many ideas in the finite element can be easily used in the meshless methods. Hence, in this study, the concept of the finite element p-Version is applied in the LPIM meshfree method. The results prove that increasing degrees of freedom limits artificial numerical oscillations occurred in very large Peclet numbers.
    Keywords: convection-diffusion problems, LPIM meshless method, natural stabilization, p-Version finite element method
  • Maryam Ramezani *, Hamid Baghani Pages 23-28
    Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theorem is a real generalization of these fixed point theorems.
    Keywords: strongly orthogonal set, fixed point, gauge function
  • Mohammad Hadi Alaeiyan*, Hamed Karami Pages 29-35
    In this paper, we enumerate the parameter matrices of all perfect 2-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and the icosahedral graph.
    Keywords: Perfect Coloring, Equitable Partition, Platonic Graph
  • Mohammad Mehdizadeh Khalsaraei * Pages 37-46
    When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) positivity is not ensured when applied to the inhomogeneous linear systems and the same result is regained on nonlinear positivity for this method. Here we mean by positivity that the nonnegativity of the components of the initial vector is preserved. Nonstandard finite differences (NSFDs) schemes can improve the accuracy and reduce computational costs of traditional finite difference schemes. In addition to NSFDs produce numerical solutions which also exhibit essential properties of solution. In this paper, we investigate the positivity property for nonstandard RK3 method when applied to the numerical solution of special nonlinear initial value problems (IVPs) for ordinary differential equations (ODEs). We obtain new results for positivity which are important in practical applications. We provide some numerical examples to illustrate our results.
    Keywords: Positivity, Initial value problems, Advection equation, Berger's equation, Runge-Kutta methods
  • Esa Sharahi, Esmaeil Peyghan *, Constantin Arcus Pages 47-63
    Considering prolongation of a Lie algebroid equipped with a spray, defining some classical tensors, we show that a Lie symmetry of a spray is a curvature collineation for these tensors.
    Keywords: Curvature collineation, Lie algebroid, Lie symmetry, projectable section, spray
  • Abbas Najati *, Mohammad Abdollahpour, Choonkil Park Pages 65-70
    The aim of this paper is to investigate the Hyers-Ulam stability of the linear differential equation
    y′′(x)αy′(x)βy(x)=f(x)
    in general case, where y∈C2[a,b], f∈C[a,b] and −∞
    Keywords: Hyers-Ulam stability, linear differential equation of second order
  • A. Ghareeb *, O.H. Khalil Pages 71-88
    The purpose of this paper is to introduce the concept of soft double fuzzy semi-topogenous order. Firstly, we give the definition of soft double fuzzy semi-topogenous order. Secondly, we induce a soft double fuzzy topology from a given soft double fuzzy semi-topogenous order by using soft double fuzzy interior operator.
    Keywords: soft double fuzzy topology, soft double fuzzy interior operator, soft double fuzzy semi-topogenous structure
  • Reza Ezzati *, Saeid Abbasbandy, Hossein Behforooz Pages 89-97
    In this paper, a new set of spline functions called ``Flat End Fuzzy Spline" is defined to interpolate given fuzzy data. Some important theorems on these splines together with their existence and uniqueness properties are discussed. Then numerical examples are presented to illustrate the differences between of using our spline and other interpolations that have been studied before.
    Keywords: fuzzy interpolation, extension principle, fuzzy splines
  • Seyyed Mohammad Tabatabaie *, Faranak Haghighifar Pages 99-107
    In this paper, we give an extension of the Wendel's theorem on KPC-hypergroups. We also show that every translation invariant mapping is corresponding with a unique positive measure on the KPC-hypergroup.
    Keywords: DJS-hypergroup, KPC-hypergroup, Translation Invariant Mapping, Wendel's Theorem
  • Artion Kashuri *, Rozana Liko Pages 109-124
    In the present paper, the notion of generalized (r;g,s,m,φ)-preinvex function is applied to establish some new generalizations of Ostrowski type integral inequalities via Caputo k-fractional derivatives. At the end, some applications to special means are given.
    Keywords: Ostrowski type inequality, H{o}lder's inequality, Minkowski's inequality, s-convex function in the second sense, m-invex
  • Mehdi Nadjafikhah *, Saeid Shagholi Pages 125-134
    In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive T-periodic solution which is globally asymptotically stable. For numerical simulations the fourth order Runge-Kutta method is applied to the nonlinear system of differential equations.
    Keywords: Mathematical modeling, epidemic SIRS model, positive solution, globally asymptotically stability
  • Ugur Duran *, Mehmet Acikgoz Pages 135-144
    The main goal of the present paper is to construct some families of the Carlitz's q-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's q-Bernoulli polynomials and numbers with weight (p. We then define the modified degenerate Carlitz's q-Bernoulli polynomials and numbers with weight (α,β) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz's q-Bernoulli polynomials with weight (α,β), the modified degenerate Carlitz's q-Bernoulli polynomials with weight (α,β), the Stirling numbers of the first kind and second kind.
    Keywords: Carlitz's q-Bernoulli polynomials, Stirling numbers of the first kind, Stirling numbers of the second kind, p-adic q-integral
  • Fayyaz Rouzkard *, Mohammad Imdad Pages 145-158
    In this paper, we introduce the concept of a w-compatible mappings and utilize the same to discuss the ideas of coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in the context of complex valued metric spaces besides proving existence theorems which are following by corresponding unique coupled common fixed point theorems for such mappings. Some illustrative examples are also given to substantiate our newly proved results.
    Keywords: Common fixed point, Contractive type mapping, coupled coincidence point, coupled point of coincidence, Complex valued metric space
  • Perikles Papadopoulos *, N.L. Matiadou Pages 159-168
    We consider the quasilinear Kirchhoff's problem
    utt−ϕ(x)||∇u(t)||2Δu(u)=0,x∈RN,t≥0,
    with the initial conditions u(x,0)=u0(x) and ut(x,0)=u1(x), in the case where \ N≥3,f(u)=|u|au \ and (ϕ(x))−1∈LN/2(RN)∩L∞(RN) is a positive function. The purpose of our work is to study the long time behaviour of the solution of this equation. Here, we prove the existence of a global attractor for this equation in the strong topology of the space X1=:D1,2(RN)×L2g(RN).
    We succeed to extend some of our earlier results concerning the asymptotic behaviour of the solution of the problem.
    Keywords: quasilinear hyperbolic equations, Kirchhoff strings, global attractor, generalised Sobolev spaces, weighted LpSpaces
  • Mahnaz Asgari *, Morteza Khodabin Pages 169-179
    In this article, a new numerical method based on triangular functions for solving nonlinear stochastic differential equations is presented. For this, the stochastic operational matrix of triangular functions for It\^{o} integral are determined. Computation of presented method is very simple and attractive. In addition, convergence analysis and numerical examples that illustrate accuracy and efficiency of the method are presented.
    Keywords: Brownian motion, It^{o} integral, Nonlinear stochastic differential equation, Stochastic operational matrix, Triangular function
  • Khursheed J. *. Ansari, Ali Karaisa Pages 181-200
    In the present article, we introduce Chlodowsky variant of (p,q)-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function f belongs to the class LipM(α). Moreover, we also discuss convergence and rate of approximation in weighted spaces and weighted statistical approximation properties of the sequence of positive linear operators defined by us.
    Keywords: (p, q)-integers, Bernstein operators, positive linear operators, Korovkin type approximation theorem, statistical approximation
  • Rezvan Kamali, Ali Davari * Pages 201-207
    In this paper, we establish a proof for a necessary condition for multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we present the related semi parametric model.
    Keywords: Multiple objective fractional programming, Generalized n-set convex function, Efficient solution
  • Mehmet Zeki Sarikaya, Huseyin Budak* Pages 209-222
    In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.
    Keywords: Generalized Hermite-Hadamard inequality, Generalized H{o}lder inequality, Generalized convex functions
  • Tayyebe Haqiri *, Azim Rivaz, Mahmoud Mohseni Moghadam Pages 223-241
    This paper introduces the \emph{interval unilateral quadratic matrix equation}, \IUQe and attempts to find various analytical results on its AE-solution sets in which \A,\B and \CCC are known real interval matrices, while X is an unknown matrix. These results are derived from a generalization of some results of Shary. We also give sufficient conditions for non-emptiness of some quasi-solution sets, provided that \A is regular. As the most common case, the united solution set has been studied and two direct methods for computing an outer estimation and an inner estimation of the united solution set of an interval unilateral quadratic matrix equation are proposed. The suggested techniques are based on nonlinear programming as well as sensitivity analysis.
    Keywords: AE-solution sets, interval unilateral quadratic matrix equation, united solution set, nonlinear programming, sensitivity analysis
  • Betul Atay, Aysun Aytac * Pages 243-250
    An exponential dominating set of graph G=(V,E) is a subset S⊆V(G) such that ∑u∈S(1/2)d¯¯¯(u,v)−1≥1 for every vertex v in V(G)−S, where d¯¯¯(u,v) is the distance between vertices u∈S and v∈V(G)−S in the graph G−(S−{u}). The exponential domination number, γe(G), is the smallest cardinality of an exponential dominating set. Graph operations are important methods for constructing new graphs, and they play key roles in the design and analysis of networks. In this study, we consider the exponential domination number of graph operations including edge corona, neighborhood corona and power.
    Keywords: Graph vulnerability, network design, communication, exponential domination number, edge corona, neighbourhood corona
  • Abdelhakim Maaden *, Stouti Abdelkader Pages 251-261
    In this paper we prove that if X is a Banach space, then for every lower semi-continuous bounded below function f, there exists a (φ1,φ2)-convex function g, with arbitrarily small norm, such that f attains its strong minimum on X.
    This result extends some of the well-known varitional principles as that of Ekeland [On the variational principle, J. Math. Anal. Appl. 47 (1974) 323--353], that of Borwein-Preiss [A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions, Trans. Amer. Math. Soc. 303 (1987) 517--527] and that of Deville-Godefroy-Zizler [Un principe variationel utilisant des fonctions bosses, C. R. Acad. Sci. (Paris). Ser.I 312 (1991) 281--286] and [A smooth variational principle with applications to Hamilton-Jacobi equations in infinite dimensions, J. Funct. Anal. 111 (1993) 197--212].
    Keywords: left(varphi1, varphi2right)-convex function, left(varphi1, varphi2right)-variational principle, Ekeland's variational principle, smooth variational principle
  • Cristian Chifu *, Gabriela Petrusel Pages 263-276
    The purpose of this paper is to present some coupled fixed point results on a metric space endowed with two b-metrics. We shall apply a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces endowed with directed graphs. Data dependence, well-posedness and Ulam-Hyers stability are also studied. The results obtained here will be applied to prove the existence and uniqueness of the solution for a system of integral equations.
    Keywords: fixed point, coupled fixed point, b-metric space, connected graph, integral equations
  • Yadollah Ordokhani *, Parisa Rahimkhani, Esmail Babolian Pages 277-292
    In this paper, a new numerical method for solving the fractional Riccati differential equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon fractional-order Bernoulli functions approximations. First, the fractional-order Bernoulli functions and their properties are presented. Then, an operational matrix of fractional order integration is derived and is utilized to reduce the under study problem to a system of algebraic equations. Error analysis included the residual error estimation and the upper bound of the absolute errors are introduced for this method. The technique and the error analysis are applied to some problems to demonstrate the validity and applicability of our method.
    Keywords: Fractional Riccati differential equation, Fractional-order Bernoulli functions, Caputo derivative, Operational matrix, Collocation method
  • Akindele Adebayo Mebawondu *, Lateef Jolaoso, Hammed Abass Pages 293-306
    In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and Δ-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this paper extend and generalize corresponding results on uniformly convex Banach spaces, CAT(0) spaces and many other results in this direction.
    Keywords: Banach operator, uniformly convex hyperbolic spaces, strong, Delta-convergence theorem, Modified Picard Normal S-iteration
  • Rashwan Rashwan *, S.M. Saleh Pages 307-326
    The aim of this paper is to prove some common fixed point theorems for four mappings satisfying (ψ,φ)-weak contractions involving rational expressions in ordered partial metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give two examples to illustrate our results.
    Keywords: Common fixed point, rational contractions, ordered partial metric spaces, dominating, dominated mappings
  • Alireza Pourmoslemi, Kourosh Nourouzi * Pages 327-333
    In this paper, we give a probabilistic counterpart of Mazur-Ulam theorem in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.
    Keywords: Probabilistic normed groups, Invariant probabilistic metrics, Mazur-Ulam Theorem
  • Shaoyuan Xu *, Suyu Cheng, Suzana Aleksic Pages 335-353
    In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assumption of normality we establish common fixed point theorems for the generalized quasi-contractions with the spectral radius r(λ) of the quasi-contractive constant vector λ satisfying r(λ)∈[0,1s) in the setting of cone b-metric spaces over Banach algebras, where the coefficient s satisfies s≥1. As consequences, we obtain common fixed point theorems for the generalized g-quasi-contractions in the setting of such spaces. The main results generalize, extend and unify several well-known comparable results in the literature. Moreover, we apply our main results to some nonlinear equations, which shows that these results are more general than corresponding ones in the setting of b-metric or metric spaces.
    Keywords: cone b-metric spaces over Banach algebras, non-normal cones, c-sequences, generalized quasi-contractions, fixed point theorem
  • Ahmad Zireh * Pages 355-362
    Let f(z) be an analytic function on the unit disk {z∈C, |z|≤1}, for each q>0, the ∥f∥q is defined as follows
    ∥f∥q:={12π∫2π0∣∣f(eiθ)∣∣qdθ}1/q, 00, ∥p′∥q≤n∥k∥q∥p∥q.
    In this paper, we shall present an interesting generalization and refinement of this result which include some previous results.
    Keywords: Derivative, Polynomial, Lq Inequality, Maximum modulus, Restricted Zeros
  • Abu Alhalawa Muna, Mohammad Saleh* Pages 363-379
    The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation
    xn=αβxnAܙ︋−k, n=0,1,2,…,
    where the parameters α, β, A, B and C are positive, and the initial conditions x−k,x−k,…,x−1,x0 are positive real numbers and k∈{1,2,3,…}. We give a detailed description of the semi-cycles of solutions and determine conditions under which the equilibrium points are globally asymptotically stable. In particular, our paper is a generalization of the rational difference equation that was investigated by Kulenovic et al. [The Dynamics of xn=αβxnAܙ︋−1
    , Facts and Conjectures, Comput. Math. Appl. 45 (2003) 1087--1099].
    Keywords: stability theory, semi-cycle analysis, invariant intervals, nonlinear difference equations, discrete dynamical systems