IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.859.1153 Research Paper Existence of common best proximity points of generalized \$S\$-proximal contractions Existence of common best proximity points Nashine Hemant Department of Mathematics, Texas A \& M University-Kingsville-78363-8202, Texas, USA Kadelburg Zoran University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia 01 12 2017 8 2 1 8 25 07 2015 28 01 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2764.html

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.

common best proximity point optimal approximate solution proximally commuting mappings
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2016.466 Research Paper On the natural stabilization of convection diffusion problems using LPIM meshless method On the natural stabilization of convection diffusion problems Arefmanesh Ali Department of Mechanical Engineering, University of Kashan, Kashan, Iran Abbaszadeh Mahmoud School of Engineering, University of Warwick, Coventry, United Kingdom 07 12 2017 8 2 9 22 03 12 2015 14 08 2016 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_466.html

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.

convection-diffusion problems LPIM meshless method natural stabilization \$p\$-Version finite element method
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2016.452 Research Paper Contractive gauge functions in strongly orthogonal metric spaces Contractive gauge functions in strongly orthogonal metric spaces Ramezani Maryam Department of Mathematics, Faculty of Mathematics, University of Bojnord, Bojnord, Iran Baghani Hamid Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran 03 12 2017 8 2 23 28 07 11 2015 07 04 2016 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_452.html

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.

strongly orthogonal set Fixed point gauge function
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2016.455 Research Paper Perfect \$2\$-colorings of the Platonic graphs Perfect \$2\$-colorings of the Platonic graphs Alaeiyan Mohammad Hadi School of Computer Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran Karami Hamed School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran 04 12 2017 8 2 29 35 23 10 2015 18 05 2016 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_455.html

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.

Perfect Coloring Equitable Partition Platonic Graph
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2016.480 Research Paper Nonstandard explicit third-order Runge-Kutta method with positivity property Nonstandard explicit third-order Runge-Kutta method Mehdizadeh Khalsaraei Mohammad Department of Mathematics, Faculty of Science, University of Maragheh, 55181-83111 Maragheh, Iran 01 12 2017 8 2 37 46 09 12 2014 20 08 2015 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_480.html

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.

Positivity Initial value problems Advection equation Bergers&#039; equation Runge-Kutta methods
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2016.516 Research Paper Curvature collineations on Lie algebroid structure Curvature collineations on Lie algebroid structure Sharahi Esa Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran Peyghan Esmaeil Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran Arcus Constantin Secondary School &quot;Cornelius Radu&quot;, Radinesti Village, 217196 Gorj County, Romania 01 12 2017 8 2 47 63 16 12 2015 16 09 2016 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_516.html

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.

Curvature collineation Lie algebroid Lie symmetry projectable section spray
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.1078.1226 Research Paper On the stability of linear differential equations of second order On the stability of linear differential equations of second order Najati Abbas Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran Abdollahpour Mohammad Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran Park Choonkil Department of Mathematics, Hanyang University, Seoul, 133--791, South Korea 06 12 2017 8 2 65 70 21 12 2015 04 06 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2768.html

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 \$yin C^2[a,b],\$  \$fin 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].

Hyers-Ulam stability linear differential equation of second order
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.1787.1469 Research Paper Soft double fuzzy semi-topogenous structures Soft double fuzzy semi-topogenous structures Ghareeb A. Department of Mathematics, Colleges of Science, Al-Baha University, Al-Baha, Saudi Arabia Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt Khalil O.H. Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt 01 12 2017 8 2 71 88 08 12 2016 27 08 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2788.html

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.

soft double fuzzy topology soft double fuzzy interior operator soft double fuzzy semi-topogenous structure
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.1419.1363 Research Paper Interpolation of fuzzy data by using flat end fuzzy splines Interpolation of fuzzy data by using flat end fuzzy splines Ezzati Reza Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran Abbasbandy Saeid Department of Applied Mathematics, Imam Khomeini International University, Qazvin, Iran Behforooz Hossein Department of Mathematics, Utica College, Utica, New York, 13502, USA 01 12 2017 8 2 89 97 03 06 2016 06 04 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2765.html

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.

fuzzy interpolation extension principle fuzzy splines
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.1365.1340 Research Paper Translation invariant mappings on KPC-hypergroups Translation invariant mappings on KPC-hypergroups Tabatabaie Seyyed Mohammad Department of Mathematics, University of Qom, Qom, Iran Haghighifar Faranak Department of Mathematics, University of Qom, Qom, Iran 01 12 2017 8 2 99 107 30 04 2016 22 07 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2785.html

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.

DJS-hypergroup KPC-hypergroup Translation Invariant Mapping Wendel&#039;s Theorem
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.11722.1585 Research Paper Some new Ostrowski type fractional integral inequalities for generalized \$(r;g,s,m,varphi)\$-preinvex functions via Caputo \$k\$-fractional derivatives Some new Ostrowski type fractional integral inequalities Kashuri Artion Department of Mathematics, Faculty of Technical Science, University &quot;Ismail Qemali&quot;, 9400, Vlora, Albania Liko Rozana Department of Mathematics, Faculty of Technical Science, University &quot;Ismail Qemali&quot;, 9400, Vlora, Albania 01 12 2017 8 2 109 124 21 06 2017 26 09 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2790.html

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.

Ostrowski type inequality H"{o}lder's inequality Minkowski's inequality \$s\$-convex function in the second sense \$m\$-invex
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.11821.1592 Research Paper Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution Mathematical modeling of optimized SIRS epidemic model Nadjafikhah Mehdi Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran Shagholi Saeid Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran 01 12 2017 8 2 125 134 04 03 2017 17 09 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2792.html

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.

Mathematical modeling epidemic SIRS model positive solution globally asymptotically stability
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.11767.1588 Research Paper Modified degenerate Carlitz's \$q\$-bernoulli polynomials and numbers with weight (\$alpha ,beta \$) Modified degenerate Carlitz's \$q\$-bernoulli polynomials Duran Ugur Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey Acikgoz Mehmet Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey 01 12 2017 8 2 135 144 27 06 2017 26 09 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2791.html

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.

Carlitz's \$q\$-Bernoulli polynomials Stirling numbers of the first kind Stirling numbers of the second kind \$p\$-adic \$q\$-integral
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.521 Research Paper Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces Coupled coincidence point and common coupled fixed point theorems Rouzkard Fayyaz Farhangian University, Shariati Pardis, Sari, Mazandaran Iran Imdad Mohammad Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India 01 12 2017 8 2 145 158 24 11 2015 08 12 2016 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_521.html

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.

Common fixed point Contractive type mapping coupled coincidence point coupled point of coincidence Complex valued metric space
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.11600.1575 Research Paper Global attractor for a nonlocal hyperbolic problem on \${mathcal{R}}^{N}\$ Global attractor for a nonlocal hyperbolic problem on \${mathcal{R}}^{N}\$ Papadopoulos Perikles Department of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece Matiadou N.L. Department of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece 01 12 2017 8 2 159 168 09 06 2017 26 09 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2793.html

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.

quasilinear hyperbolic equations Kirchhoff strings global attractor generalised Sobolev spaces weighted \$L^p\$ Spaces
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.1023.1198 Research Paper Computational method based on triangular operational matrices for solving nonlinear stochastic differential equations Computational method based on triangular operational matrices Asgari Mahnaz Department of Engineering,~Abhar Branch,~Islamic Azad University, Abhar, Iran khodabin Morteza Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran 01 12 2017 8 2 169 179 22 11 2015 04 06 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2783.html

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.

Brownian motion It^{o} integral Nonlinear stochastic differential equation Stochastic operational matrix Triangular function
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.1827.1479 Research Paper On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators On the approximation by Chlodowsky type generalization Ansari Khursheed J. Department of Mathematics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia Karaisa Ali Department of Mathematics-Computer Sciences, Faculty of Sciences, Necmettin Erbakan University Meram Campus, 42090 Meran, Konya, Turkey 01 12 2017 8 2 181 200 27 12 2016 25 09 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2789.html

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.

\$(p,q)\$-integers Bernstein operators positive linear operators Korovkin type approximation theorem statistical approximation
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2016.482 Research Paper A necessary condition for multiple objective fractional programming A necessary condition for multiple objective fractional programming Kamali Rezvan Department of Mathematics, Faculty of Science, University of Isfahan, Isfahan, Iran Davari Ali Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran 01 12 2017 8 2 201 207 19 01 2015 05 08 2015 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_482.html

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.

Multiple objective fractional programming Generalized n-set convex function Efficient solution
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.11313.1552 Research Paper On generalized Hermite-Hadamard inequality for generalized convex function On generalized Hermite-Hadamard inequality Sarikaya Mehmet Zeki Department of Mathematics, Faculty of Science and Arts, D\&quot;{u}zce University, D\&quot;{u}zce-Turkey Budak Huseyin Department of Mathematics, Faculty of Science and Arts, D\&quot;{u}zce University, D\&quot;{u}zce-Turkey 01 12 2017 8 2 209 222 11 05 2017 18 10 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2797.html

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.

Generalized Hermite-Hadamard inequality Generalized H"{o}lder inequality Generalized convex functions
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.10778.1523 Research Paper Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets Analytical aspects of the interval unilateral quadratic matrix equations Haqiri Tayyebe 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 Rivaz Azim Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran Mohseni Moghadam Mahmoud Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran 20 12 2017 8 2 223 241 07 03 2017 26 09 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2796.html

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.

AE-solution sets interval unilateral quadratic matrix equation united solution set nonlinear programming Sensitivity analysis
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.3056.1494 Research Paper On exponential domination and graph operations On exponential domination and graph operations Atay Betul Department of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, Turkey Aytac Aysun Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova-Izmir, Turkey 01 12 2017 8 2 243 250 19 01 2017 04 06 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2767.html

An exponential dominating set of graph \$G = (V,E )\$ is a subset \$Ssubseteq V(G)\$ such that \$sum_{uin 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.

Graph vulnerability network design and communication exponential domination number edge corona neighbourhood corona
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.1664.1439 Research Paper \$(varphi_1, varphi_2)\$-variational principle \$(varphi_1, varphi_2)\$-variational principle Maaden Abdelhakim 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, Maroc Abdelkader Stouti 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, Maroc 22 12 2017 8 2 251 261 13 10 2016 09 05 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2766.html

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_2right)\$-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].

\$left(varphi_1, varphi_2right)\$-convex function \$left(varphi_1, varphi_2right)\$-variational principle Ekeland's variational principle smooth variational principle
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.11562.1570 Research Paper Existence and uniqueness of the solution for a general system of operator equations in \$b-\$metric spaces endowed with a graph Existence and uniqueness of the solution for a general system Chifu Cristian Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania Petrusel Gabriela Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania 23 12 2017 8 2 263 276 06 06 2017 11 11 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2800.html

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.

Fixed point Coupled fixed point \$b\$-metric space connected graph integral equations
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.1476.1379 Research Paper Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation Application of fractional-order Bernoulli functions Ordokhani Yadollah Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran Rahimkhani Parisa Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran National Elites Foundation, Tehran, Iran Babolian Esmail Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran 01 12 2017 8 2 277 292 29 06 2016 26 09 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2795.html

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.

Fractional Riccati differential equation Fractional-order Bernoulli functions Caputo derivative Operational matrix Collocation method
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.11887.1594 Research Paper On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces On some fixed points properties and convergence theorems Mebawondu Akindele Adebayo School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa Jolaoso Lateef School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa Abass Hammed School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa 01 12 2017 8 2 293 306 09 07 2017 23 10 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2799.html

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.

Banach operator uniformly convex hyperbolic spaces strong and \$Delta\$-convergence theorem Modified Picard Normal S-iteration
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2016.468 Research Paper Some common fixed point theorems for four \$(psi,varphi)\$-weakly contractive mappings satisfying rational expressions in ordered partial metric spaces Some common fixed point theorems for four \$(psi,varphi)\$-weakly contractive mappings Rashwan Rashwan Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt Saleh S.M. Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt 26 12 2017 8 2 307 326 30 07 2013 24 12 2015 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_468.html

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.

Common fixed point rational contractions ordered partial metric spaces dominating and dominated mappings
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.1281.1318 Research Paper Mazur-Ulam theorem in probabilistic normed groups Mazur-Ulam theorem in probabilistic normed groups Pourmoslemi Alireza Department of Mathematics, Payame Noor University, Tehran, Iran Nourouzi Kourosh Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran 01 12 2017 8 2 327 333 23 03 2016 21 07 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2786.html

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.

Probabilistic normed groups Invariant probabilistic metrics Mazur-Ulam Theorem
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.1857.1483 Research Paper Fixed point theorems for generalized quasi-contractions in cone \$b\$-metric spaces over Banach algebras without the assumption of normality with applications Fixed point theorems for generalized quasi-contractions Xu Shaoyuan School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China Cheng Suyu Library, Hanshan Normal University, Chaozhou, 521041, China Aleksic Suzana Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovi\&#039;ca 12, 34000 Kragujevac, Serbia 01 12 2017 8 2 335 353 08 01 2017 27 08 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2787.html

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 \$sge 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.

cone \$b\$-metric spaces over Banach algebras non-normal cones \$c\$-sequences generalized quasi-contractions Fixed point theorem
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.1286.1321 Research Paper L\$^q\$ inequalities for the \${s^{th}}\$ derivative of a polynomial L\$^q\$ inequalities for the \${s^{th}}\$ derivative of a polynomial Zireh Ahmad Department of Mathematics, Shahrood University of Technology, Shahrood, Iran 01 12 2017 8 2 355 362 02 04 2016 01 10 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2801.html

Let \$f(z)\$ be an analytic function on the unit disk \${zinmathbb{C}, |z|leq 1}\$, for each \$q>0\$, the \$|f|_{q}\$ is defined as followsbegin{align*}begin{split}&left|fright|_q:=left{frac{1}{2pi}int_0^{2pi}left|f(e^{itheta})right|^qdthetaright}^{1/q}, 0<q<infty,\&left|fright|_{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 \$kgeq 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.

Derivative Polynomial \$L^q\$ Inequality Maximum modulus Restricted Zeros
IJNAA Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Semnan University 4 10.22075/ijnaa.2017.10822.1526 Research Paper Dynamics of higher order rational difference equation \$x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})\$ Dynamics of higher order rational difference equation Muna Abu Alhalawa Department of Mathematics, Faculty of Science, Birzeit University, Palestine Saleh Mohammad Department of Mathematics, Faculty of Science, Birzeit University, Palestine 01 12 2017 8 2 363 379 11 03 2017 26 09 2017 Copyright © 2017, Semnan University. 2017 https://ijnaa.semnan.ac.ir/article_2794.html

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 \$kin{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].

stability theory semi-cycle analysis invariant intervals nonlinear difference equations discrete dynamical systems