Existence of common best proximity points of generalized $S$-proximal contractions Hemant Nashine Department of Mathematics, Texas A & M University-Kingsville-78363-8202, Texas, USA author Zoran Kadelburg University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 1 8 https://ijnaa.semnan.ac.ir/article_2764_4a0f5785686f6c06e1cccf3bf040f1c4.pdf dx.doi.org/10.22075/ijnaa.2017.859.1153 On the natural stabilization of convection diffusion problems using LPIM meshless method Ali Arefmanesh Department of Mechanical Engineering, University of Kashan, Kashan, Iran author Mahmoud Abbaszadeh School of Engineering, University of Warwick, Coventry, United Kingdom author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 9 22 https://ijnaa.semnan.ac.ir/article_466_bbb3a1fc16ee7db611610410e3835c9f.pdf dx.doi.org/10.22075/ijnaa.2016.466 Contractive gauge functions in strongly orthogonal metric spaces Maryam Ramezani Department of Mathematics, Faculty of Mathematics, University of Bojnord, Bojnord, Iran author Hamid Baghani Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 23 28 https://ijnaa.semnan.ac.ir/article_452_2a1a25491ed3b19576dc43dcff80d39b.pdf dx.doi.org/10.22075/ijnaa.2016.452 Perfect $2$-colorings of the Platonic graphs Mohammad Hadi Alaeiyan School of Computer Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran author Hamed Karami School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 29 35 https://ijnaa.semnan.ac.ir/article_455_b232654319dc2a0cb031bc04091ece3d.pdf dx.doi.org/10.22075/ijnaa.2016.455 Nonstandard explicit third-order Runge-Kutta method with positivity property Mohammad Mehdizadeh Khalsaraei Department of Mathematics, Faculty of Science, University of Maragheh, 55181-83111 Maragheh, Iran author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 37 46 https://ijnaa.semnan.ac.ir/article_480_bfe54710147d214731391df012a6a25a.pdf dx.doi.org/10.22075/ijnaa.2016.480 Curvature collineations on Lie algebroid structure Esa Sharahi Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran author Esmaeil Peyghan Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran author Constantin Arcus Secondary School &quot;Cornelius Radu&quot;, Radinesti Village, 217196 Gorj County, Romania author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 47 63 https://ijnaa.semnan.ac.ir/article_516_59906f46ca9f8631db7aac16657b95ac.pdf dx.doi.org/10.22075/ijnaa.2016.516 On the stability of linear differential equations of second order Abbas Najati Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran author Mohammad Abdollahpour Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran author Choonkil Park Department of Mathematics, Hanyang University, Seoul, 133--791, South Korea author text article 2017 eng The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+\alpha y'(x)+\beta y(x)=f(x)$$in general case, where $y\in C^2[a,b],$  $f\in C[a,b]$ and $-\infty<a<b<+\infty$. The result of this paper improves a result of Li and Shen [\textit{Hyers-Ulam stability of linear differential equations of second order,} Appl. Math. Lett. 23 (2010) 306--309]. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 65 70 https://ijnaa.semnan.ac.ir/article_2768_c56749cc1ab49441e4b381aa39b132e9.pdf dx.doi.org/10.22075/ijnaa.2017.1078.1226 Soft double fuzzy semi-topogenous structures A. Ghareeb Department of Mathematics, Colleges of Science, Al-Baha University, Al-Baha, Saudi Arabia author O.H. Khalil Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 71 88 https://ijnaa.semnan.ac.ir/article_2788_42478fba2bdf9494bd980f7308e1f221.pdf dx.doi.org/10.22075/ijnaa.2017.1787.1469 Interpolation of fuzzy data by using flat end fuzzy splines Reza Ezzati Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran author Saeid Abbasbandy Department of Applied Mathematics, Imam Khomeini International University, Qazvin, Iran author Hossein Behforooz Department of Mathematics, Utica College, Utica, New York, 13502, USA author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 89 97 https://ijnaa.semnan.ac.ir/article_2765_d76b656bd725808a80f0451c76bd26b8.pdf dx.doi.org/10.22075/ijnaa.2017.1419.1363 Translation invariant mappings on KPC-hypergroups Seyyed Mohammad Tabatabaie Department of Mathematics, University of Qom, Qom, Iran author Faranak Haghighifar Department of Mathematics, University of Qom, Qom, Iran author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 99 107 https://ijnaa.semnan.ac.ir/article_2785_050eaa7a4eae270a339a107852a64608.pdf dx.doi.org/10.22075/ijnaa.2017.1365.1340 Some new Ostrowski type fractional integral inequalities for generalized $(r;g,s,m,\varphi)$-preinvex functions via Caputo $k$-fractional derivatives Artion Kashuri Department of Mathematics, Faculty of Technical Science, University &quot;Ismail Qemali&quot;, 9400, Vlora, Albania author Rozana Liko Department of Mathematics, Faculty of Technical Science, University &quot;Ismail Qemali&quot;, 9400, Vlora, Albania author text article 2017 eng In the present paper, the notion of generalized $(r;g,s,m,\varphi)$-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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 109 124 https://ijnaa.semnan.ac.ir/article_2790_0b41c4fb5b26b287e9fc35c76b4ec926.pdf dx.doi.org/10.22075/ijnaa.2017.11722.1585 Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution Mehdi Nadjafikhah Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran author Saeid Shagholi Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 125 134 https://ijnaa.semnan.ac.ir/article_2792_035182d58bb9842edde0597201b211da.pdf dx.doi.org/10.22075/ijnaa.2017.11821.1592 Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta$) Ugur Duran Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey author Mehmet Acikgoz Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey author text article 2017 eng 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 ($\alpha ,\beta$) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz's $q$-Bernoulli polynomials with weight ($\alpha ,\beta$), the modified degenerate Carlitz's $q$-Bernoulli polynomials with weight ($\alpha ,\beta$), the Stirling numbers of the first kind and second kind. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 135 144 https://ijnaa.semnan.ac.ir/article_2791_48a0eba5d8560ea93b810f1b3562b4eb.pdf dx.doi.org/10.22075/ijnaa.2017.11767.1588 Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces Fayyaz Rouzkard Farhangian University, Shariati Pardis, Sari, Mazandaran Iran author Mohammad Imdad Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 145 158 https://ijnaa.semnan.ac.ir/article_521_2a61f222299a2c5adf3e26b8819aaa3a.pdf dx.doi.org/10.22075/ijnaa.2017.521 Global attractor for a nonlocal hyperbolic problem on ${\mathcal{R}}^{N}$ Perikles Papadopoulos Department of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece author N.L. Matiadou Department of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece author text article 2017 eng We consider the quasilinear Kirchhoff's problem$$u_{tt}-\phi (x)||\nabla u(t)||^{2}\Delta u+f(u)=0 ,\;\; x \in {\mathcal{R}}^{N}, \;\; t \geq 0,$$with the initial conditions  $u(x,0) = u_0 (x)$  and $u_t(x,0) = u_1 (x)$, in the case where \ $N \geq 3, \; f(u)=|u|^{a}u$ \ and $(\phi (x))^{-1} \in L^{N/2}({\mathcal{R}}^{N})\cap L^{\infty}({\mathcal{R}}^{N} )$ 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 ${\cal X}_{1}=:{\cal D}^{1,2}({\mathcal{R}}^{N}) \times L^{2}_{g}({\mathcal{R}}^{N}).$ We succeed to extend some of our earlier results concerning the asymptotic behaviour of the solution of the problem. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 159 168 https://ijnaa.semnan.ac.ir/article_2793_ef30a57e5aaa4eb687c61b37a80ea4d1.pdf dx.doi.org/10.22075/ijnaa.2017.11600.1575 Computational method based on triangular operational matrices for solving nonlinear stochastic differential equations Mahnaz Asgari Department of Engineering,~Abhar Branch,~Islamic Azad University, Abhar, Iran author Morteza khodabin Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 169 179 https://ijnaa.semnan.ac.ir/article_2783_c6fbfe31fd6236b020f1a1ec4c88ae52.pdf dx.doi.org/10.22075/ijnaa.2017.1023.1198 On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators Khursheed Ansari Department of Mathematics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia author Ali Karaisa Department of Mathematics-Computer Sciences, Faculty of Sciences, Necmettin Erbakan University Meram Campus, 42090 Meran, Konya, Turkey author text article 2017 eng 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 Lip$_{M}(\alpha )$. 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 181 200 https://ijnaa.semnan.ac.ir/article_2789_8c00a08033e702b77e6d822b3272f202.pdf dx.doi.org/10.22075/ijnaa.2017.1827.1479 A necessary condition for multiple objective fractional programming Rezvan Kamali Department of Mathematics, Faculty of Science, University of Isfahan, Isfahan, Iran author Ali Davari Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 201 207 https://ijnaa.semnan.ac.ir/article_482_73a53fecfb7bfc8a6778a60cabed4272.pdf dx.doi.org/10.22075/ijnaa.2016.482 On generalized Hermite-Hadamard inequality for generalized convex function Mehmet Zeki Sarikaya Department of Mathematics, Faculty of Science and Arts, D\&quot;{u}zce University, D\&quot;{u}zce-Turkey author Huseyin Budak Department of Mathematics, Faculty of Science and Arts, D\&quot;{u}zce University, D\&quot;{u}zce-Turkey author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 209 222 https://ijnaa.semnan.ac.ir/article_2797_fe30c34bcf477187700e2c4e5c003604.pdf dx.doi.org/10.22075/ijnaa.2017.11313.1552 Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets Tayyebe Haqiri School of Mathematics and Computer Science, Damghan University, Damghan, Iran; Member of Young Researchers Society of Shahid Bahonar University of Kerman, Kerman, P.O. Box 76169-14111, Iran author Azim Rivaz Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran author Mahmoud Mohseni Moghadam Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran author text article 2017 eng This paper introduces the interval unilateral quadratic matrix equation, $AX^2+BX+C=0$ and attempts to find various analytical results on its $AE$-solution sets in which $A, B$ and $C$ 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 223 241 https://ijnaa.semnan.ac.ir/article_2796_50bf006dbe46ff6c42b14348865a347c.pdf dx.doi.org/10.22075/ijnaa.2017.10778.1523 On exponential domination and graph operations Betul Atay Department of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, Turkey author Aysun Aytac Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova-Izmir, Turkey author text article 2017 eng An exponential dominating set of graph $G = (V,E )$ is a subset $S\subseteq V(G)$ such that $\sum_{u\in S}(1/2)^{\overline{d}{(u,v)-1}}\geq 1$ for every vertex $v$ in $V(G)-S$, where $\overline{d}(u,v)$ is the distance between vertices $u \in S$ and $v \in V(G)-S$ in the graph $G -(S-\{u\})$. The exponential domination number, $\gamma_{e}(G)$, 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 243 250 https://ijnaa.semnan.ac.ir/article_2767_30d3be476f5e7e4708605bbc92f6406d.pdf dx.doi.org/10.22075/ijnaa.2017.3056.1494 $(\varphi_1, \varphi_2)$-variational principle Abdelhakim Maaden Universit&#039;e Sultan Moulay Slimane, Facult&#039;e des Sciences et Techniques, Laboratoire de Math&#039;ematiques et Applications, B.P. 523, Beni-Mellal 23000, Marocco author Stouti Abdelkader Universit&#039;e Sultan Moulay Slimane, Facult&#039;e des Sciences et Techniques, Laboratoire de Math&#039;ematiques et Applications, B.P. 523, Beni-Mellal 23000, Marocco author text article 2017 eng 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 $\left(\varphi_1, \varphi_2\right)$-convex function $g,$ with arbitrarily small norm,  such that $f + g$ 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]. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 251 261 https://ijnaa.semnan.ac.ir/article_2766_da52f80c47f3aee56ce7052c87770f23.pdf dx.doi.org/10.22075/ijnaa.2017.1664.1439 Existence and uniqueness of the solution for a general system of operator equations in $b-$metric spaces endowed with a graph Cristian Chifu Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania author Gabriela Petrusel Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 263 276 https://ijnaa.semnan.ac.ir/article_2800_62e25ec2b3418aa3f744b6478d9fbcde.pdf dx.doi.org/10.22075/ijnaa.2017.11562.1570 Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation Yadollah Ordokhani Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran author Parisa Rahimkhani Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran National Elites Foundation, Tehran, Iran author Esmail Babolian Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 277 292 https://ijnaa.semnan.ac.ir/article_2795_3990006fa9915eb0af3345e8046f7bc8.pdf dx.doi.org/10.22075/ijnaa.2017.1476.1379 On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces Akindele Adebayo Mebawondu School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa author Lateef Jolaoso School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa author Hammed Abass School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa author text article 2017 eng 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 $\Delta$-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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 293 306 https://ijnaa.semnan.ac.ir/article_2799_2ea33223c55fba3700f88bd7aefc3695.pdf dx.doi.org/10.22075/ijnaa.2017.11887.1594 Some common fixed point theorems for four $(\psi,\varphi)$-weakly contractive mappings satisfying rational expressions in ordered partial metric spaces Rashwan Rashwan Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt author S.M. Saleh Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt author text article 2017 eng The aim of this paper is to prove some common fixed point theorems for four  mappings satisfying $(\psi,\varphi)$-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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 307 326 https://ijnaa.semnan.ac.ir/article_468_a5b9c5cc09ff9b3a978f98266a1b155a.pdf dx.doi.org/10.22075/ijnaa.2016.468 Mazur-Ulam theorem in probabilistic normed groups Alireza Pourmoslemi Department of Mathematics, Payame Noor University, Tehran, Iran author Kourosh Nourouzi Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran author text article 2017 eng 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 327 333 https://ijnaa.semnan.ac.ir/article_2786_313d118769848a5d41636e321e9950d6.pdf dx.doi.org/10.22075/ijnaa.2017.1281.1318 Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications Shaoyuan Xu School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China author Suyu Cheng Library, Hanshan Normal University, Chaozhou, 521041, China author Suzana Aleksic Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovi&#039;ca 12, 34000 Kragujevac, Serbia author text article 2017 eng 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 $r(\lambda)$ of the quasi-contractive constant vector $\lambda$ satisfying $r(\lambda)\in [0,\frac{1}{s})$  in the setting of   cone $b$-metric spaces over Banach algebras, where the coefficient $s$ satisfies $s\ge 1$. 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. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 335 353 https://ijnaa.semnan.ac.ir/article_2787_c82fdf395409faa23840674b2855da21.pdf dx.doi.org/10.22075/ijnaa.2017.1857.1483 L$^q$ inequalities for the ${s^{th}}$ derivative of a polynomial Ahmad Zireh Department of Mathematics, Shahrood University of Technology, Shahrood, Iran author text article 2017 eng Let $f(z)$ be an analytic function on the unit disk $\{z\in\mathbb{C},\ |z|\leq 1\}$, for each $q>0$, the $\|f\|_{q}$ is defined as follows\begin{align*}\begin{split}&\left\|f\right\|_q:=\left\{\frac{1}{2\pi}\int_0^{2\pi}\left|f(e^{i\theta})\right|^qd\theta\right\}^{1/q},\\ \ 0<q<\infty,\\&\left\|f\right\|_{\infty}:=\max_{|z|=1}\left|f(z)\right|.\end{split}\end{align*} Govil and Rahman [{\it Functions of exponential type not vanishing in a half-plane and related polynomials}, { Trans. Amer. Math. Soc.} {137} (1969) 501--517] proved that if $p(z)$ is a polynomial of degree $n$, which does not vanish in $|z|<k$, where $k\geq 1$, then for each $q>0$,\begin{align*}\left\|p'\right\|_{q}\leq \frac{n}{\|k+z\|_q}\|p\|_{q}.\end{align*}In this paper, we shall present an interesting generalization and refinement of this result which include some previous results. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 355 362 https://ijnaa.semnan.ac.ir/article_2801_1533fb6d1e1801bc30789ab8dc04255b.pdf dx.doi.org/10.22075/ijnaa.2017.1286.1321 Dynamics of higher order rational difference equation $x_{n+1}=(\alpha+\beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$ Abu Alhalawa Muna Department of Mathematics, Faculty of Science, Birzeit University, Palestine author Mohammad Saleh Department of Mathematics, Faculty of Science, Birzeit University, Palestine author text article 2017 eng 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$$x_{n+1}=\frac{\alpha+\beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,\ldots,$$where the parameters $\alpha$, $\beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},\ldots,x_{-1},x_{0}$ are positive real numbers and $k\in\{1,2,3,\ldots\}$. 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 $x_{n+1}=\frac{\alpha +\beta x_{n}}{A+Bx_{n}+ C x_{n-1}}$, Facts and Conjectures, Comput. Math. Appl. 45 (2003) 1087--1099]. International Journal of Nonlinear Analysis and Applications Semnan University 2008-6822 8 v. 2 no. 2017 363 379 https://ijnaa.semnan.ac.ir/article_2794_5faa22d45bfb19c931f7a566b1d51774.pdf dx.doi.org/10.22075/ijnaa.2017.10822.1526