Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Existence of common best proximity points of generalized \$S\$-proximal contractions 1 8 EN Hemant Nashine 0000-0002-0250-9172 Department of Mathematics, Texas A \& M University-Kingsville-78363-8202, Texas, USA drhknashine@gmail.com Zoran Kadelburg University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia kadelbur@matf.bg.ac.rs 10.22075/ijnaa.2017.859.1153 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 https://ijnaa.semnan.ac.ir/article_2764.html https://ijnaa.semnan.ac.ir/article_2764_4a0f5785686f6c06e1cccf3bf040f1c4.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 07 On the natural stabilization of convection diffusion problems using LPIM meshless method 9 22 EN Ali Arefmanesh Department of Mechanical Engineering, University of Kashan, Kashan, Iran arefmanesh@kashanu.ac.ir Mahmoud Abbaszadeh School of Engineering, University of Warwick, Coventry, United Kingdom m.abbaszadeh@warwick.ac.uk 10.22075/ijnaa.2016.466 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 https://ijnaa.semnan.ac.ir/article_466.html https://ijnaa.semnan.ac.ir/article_466_bbb3a1fc16ee7db611610410e3835c9f.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 03 Contractive gauge functions in strongly orthogonal metric spaces 23 28 EN Maryam Ramezani Department of Mathematics, Faculty of Mathematics, University of Bojnord, Bojnord, Iran mar.ram.math@gmail.com Hamid Baghani Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran h.baghani@gmail.com 10.22075/ijnaa.2016.452 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 https://ijnaa.semnan.ac.ir/article_452.html https://ijnaa.semnan.ac.ir/article_452_2a1a25491ed3b19576dc43dcff80d39b.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 04 Perfect \$2\$-colorings of the Platonic graphs 29 35 EN Mohammad Hadi Alaeiyan School of Computer Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran hadi_alaeiyan@comp.iust.ac.ir Hamed Karami School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran h_karami@iust.ac.ir 10.22075/ijnaa.2016.455 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 https://ijnaa.semnan.ac.ir/article_455.html https://ijnaa.semnan.ac.ir/article_455_b232654319dc2a0cb031bc04091ece3d.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Nonstandard explicit third-order Runge-Kutta method with positivity property 37 46 EN Mohammad Mehdizadeh Khalsaraei Department of Mathematics, Faculty of Science, University of Maragheh, 55181-83111 Maragheh, Iran muhammad.mehdizadeh@gmail.com 10.22075/ijnaa.2016.480 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' equation,Runge-Kutta methods https://ijnaa.semnan.ac.ir/article_480.html https://ijnaa.semnan.ac.ir/article_480_bfe54710147d214731391df012a6a25a.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Curvature collineations on Lie algebroid structure 47 63 EN Esa Sharahi Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran esasharahi@gmail.com Esmaeil Peyghan Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran epeyghan@gmail.com Constantin Arcus Secondary School "Cornelius Radu", Radinesti Village, 217196 Gorj County, Romania c_arcus@radinesti.ro 10.22075/ijnaa.2016.516 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 https://ijnaa.semnan.ac.ir/article_516.html https://ijnaa.semnan.ac.ir/article_516_59906f46ca9f8631db7aac16657b95ac.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 06 On the stability of linear differential equations of second order 65 70 EN Abbas Najati Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran a.nejati@yahoo.com Mohammad Abdollahpour Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran mrabdollahpour@yahoo.com Choonkil Park Department of Mathematics, Hanyang University, Seoul, 133--791, South Korea baak@hanyang.ac.kr 10.22075/ijnaa.2017.1078.1226 The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation<br />\$\$y''(x)+alpha y'(x)+beta y(x)=f(x)\$\$<br />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 https://ijnaa.semnan.ac.ir/article_2768.html https://ijnaa.semnan.ac.ir/article_2768_c56749cc1ab49441e4b381aa39b132e9.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Soft double fuzzy semi-topogenous structures 71 88 EN A. Ghareeb Department of Mathematics, Colleges of Science, Al-Baha University, Al-Baha, Saudi Arabia Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt a.ghareeb@sci.svu.edu.eg O.H. Khalil 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 nasserfuzt@hotmail.com 10.22075/ijnaa.2017.1787.1469 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 https://ijnaa.semnan.ac.ir/article_2788.html https://ijnaa.semnan.ac.ir/article_2788_42478fba2bdf9494bd980f7308e1f221.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Interpolation of fuzzy data by using flat end fuzzy splines 89 97 EN Reza Ezzati Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran ezati@kiau.ac.ir Saeid Abbasbandy Department of Applied Mathematics, Imam Khomeini International University, Qazvin, Iran abbasbandy@yahoo.com Hossein Behforooz Department of Mathematics, Utica College, Utica, New York, 13502, USA hbehforooz@utica.edu 10.22075/ijnaa.2017.1419.1363 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 https://ijnaa.semnan.ac.ir/article_2765.html https://ijnaa.semnan.ac.ir/article_2765_d76b656bd725808a80f0451c76bd26b8.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Translation invariant mappings on KPC-hypergroups 99 107 EN Seyyed Mohammad Tabatabaie null Department of Mathematics, University of Qom, Qom, Iran sm.tabatabaie@qom.ac.ir Faranak Haghighifar Department of Mathematics, University of Qom, Qom, Iran f.haghighifar@yahoo.com 10.22075/ijnaa.2017.1365.1340 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's Theorem https://ijnaa.semnan.ac.ir/article_2785.html https://ijnaa.semnan.ac.ir/article_2785_050eaa7a4eae270a339a107852a64608.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Some new Ostrowski type fractional integral inequalities for generalized \$(r;g,s,m,varphi)\$-preinvex functions via Caputo \$k\$-fractional derivatives 109 124 EN Artion Kashuri 0000-0003-0115-3079 Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania artionkashuri@gmail.com Rozana Liko 0000-0003-2439-8538 Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400, Vlora, Albania rozanaliko86@gmail.com 10.22075/ijnaa.2017.11722.1585 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 https://ijnaa.semnan.ac.ir/article_2790.html https://ijnaa.semnan.ac.ir/article_2790_0b41c4fb5b26b287e9fc35c76b4ec926.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution 125 134 EN Mehdi Nadjafikhah Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran m_nadjafikhah@iust.ac.ir Saeid Shagholi Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran sshagholi@mathdep.iust.ac.ir 10.22075/ijnaa.2017.11821.1592 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 https://ijnaa.semnan.ac.ir/article_2792.html https://ijnaa.semnan.ac.ir/article_2792_035182d58bb9842edde0597201b211da.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Modified degenerate Carlitz's \$q\$-bernoulli polynomials and numbers with weight (\$alpha ,beta \$) 135 144 EN Ugur Duran 0000-0002-5717-1199 Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey mtdrnugur@gmail.com Mehmet Acikgoz Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey acikgoz@gantep.edu.tr 10.22075/ijnaa.2017.11767.1588 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 https://ijnaa.semnan.ac.ir/article_2791.html https://ijnaa.semnan.ac.ir/article_2791_48a0eba5d8560ea93b810f1b3562b4eb.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces 145 158 EN Fayyaz Rouzkard Farhangian University, Shariati Pardis, Sari, Mazandaran Iran fayyazrouzkard@gmail.com Mohammad Imdad Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India mhimdad@yahoo.co.in 10.22075/ijnaa.2017.521 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 https://ijnaa.semnan.ac.ir/article_521.html https://ijnaa.semnan.ac.ir/article_521_2a61f222299a2c5adf3e26b8819aaa3a.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Global attractor for a nonlocal hyperbolic problem on \${mathcal{R}}^{N}\$ 159 168 EN 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 ppapadop@puas.gr 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 lmatiadou@yahoo.gr 10.22075/ijnaa.2017.11600.1575 We consider the quasilinear Kirchhoff's problem<br />\$\$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,\$\$<br />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 https://ijnaa.semnan.ac.ir/article_2793.html https://ijnaa.semnan.ac.ir/article_2793_ef30a57e5aaa4eb687c61b37a80ea4d1.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Computational method based on triangular operational matrices for solving nonlinear stochastic differential equations 169 179 EN Mahnaz Asgari Department of Engineering,~Abhar Branch,~Islamic Azad University, Abhar, Iran mah_sgr@yahoo.com Morteza khodabin Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran m-khodabin@kiau.ac.ir 10.22075/ijnaa.2017.1023.1198 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 https://ijnaa.semnan.ac.ir/article_2783.html https://ijnaa.semnan.ac.ir/article_2783_c6fbfe31fd6236b020f1a1ec4c88ae52.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators 181 200 EN Khursheed J. Ansari Department of Mathematics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia ansari.jkhursheed@gmail.com Ali Karaisa Department of Mathematics-Computer Sciences, Faculty of Sciences, Necmettin Erbakan University Meram Campus, 42090 Meran, Konya, Turkey akaraisa@konya.edu.tr 10.22075/ijnaa.2017.1827.1479 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 https://ijnaa.semnan.ac.ir/article_2789.html https://ijnaa.semnan.ac.ir/article_2789_8c00a08033e702b77e6d822b3272f202.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 A necessary condition for multiple objective fractional programming 201 207 EN Rezvan Kamali Department of Mathematics, Faculty of Science, University of Isfahan, Isfahan, Iran reka_math@yahoo.com Ali Davari Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran a_davari2002@yahoo.com 10.22075/ijnaa.2016.482 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 https://ijnaa.semnan.ac.ir/article_482.html https://ijnaa.semnan.ac.ir/article_482_73a53fecfb7bfc8a6778a60cabed4272.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 On generalized Hermite-Hadamard inequality for generalized convex function 209 222 EN Mehmet Zeki Sarikaya Department of Mathematics, Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce-Turkey sarikayamz@gmail.com Huseyin Budak 0000-0001-8843-955X Department of Mathematics, Faculty of Science and Arts, D\"{u}zce University, D\"{u}zce-Turkey hsyn.budak@gmail.com 10.22075/ijnaa.2017.11313.1552 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 https://ijnaa.semnan.ac.ir/article_2797.html https://ijnaa.semnan.ac.ir/article_2797_fe30c34bcf477187700e2c4e5c003604.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 20 Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets 223 241 EN 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 thaqiri@gmail.com Azim Rivaz Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran arivaz@uk.ac.ir Mahmoud Mohseni Moghadam Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran mohseni@uk.ac.ir 10.22075/ijnaa.2017.10778.1523 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 https://ijnaa.semnan.ac.ir/article_2796.html https://ijnaa.semnan.ac.ir/article_2796_50bf006dbe46ff6c42b14348865a347c.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 On exponential domination and graph operations 243 250 EN Betul Atay Department of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, Turkey btlatay87@gmail.com Aysun Aytac Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova-Izmir, Turkey aysun.aytac@ege.edu.tr 10.22075/ijnaa.2017.3056.1494 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 https://ijnaa.semnan.ac.ir/article_2767.html https://ijnaa.semnan.ac.ir/article_2767_30d3be476f5e7e4708605bbc92f6406d.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 22 \$(varphi_1, varphi_2)\$-variational principle 251 261 EN Abdelhakim Maaden Universit\'e Sultan Moulay Slimane, Facult\'e des Sciences et Techniques, Laboratoire de Math\'ematiques et Applications, B.P. 523, Beni-Mellal 23000, Maroc hmaaden2002@yahoo.fr Stouti Abdelkader Universit\'e Sultan Moulay Slimane, Facult\'e des Sciences et Techniques, Laboratoire de Math\'ematiques et Applications, B.P. 523, Beni-Mellal 23000, Maroc stouti@yahoo.com 10.22075/ijnaa.2017.1664.1439 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 https://ijnaa.semnan.ac.ir/article_2766.html https://ijnaa.semnan.ac.ir/article_2766_da52f80c47f3aee56ce7052c87770f23.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 23 Existence and uniqueness of the solution for a general system of operator equations in \$b-\$metric spaces endowed with a graph 263 276 EN Cristian Chifu Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania cristian.chifu@tbs.ubbcluj.ro Gabriela Petrusel Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania gabi.petrusel@tbs.ubbcluj.ro 10.22075/ijnaa.2017.11562.1570 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 https://ijnaa.semnan.ac.ir/article_2800.html https://ijnaa.semnan.ac.ir/article_2800_62e25ec2b3418aa3f744b6478d9fbcde.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation 277 292 EN Yadollah Ordokhani 0000-0002-5167-6874 Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran ordokhani@alzahra.ac.ir Parisa Rahimkhani Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran National Elites Foundation, Tehran, Iran p.rahimkhani@alzahra.ac.ir Esmail Babolian Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran babolian@khu.ac.ir 10.22075/ijnaa.2017.1476.1379 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 https://ijnaa.semnan.ac.ir/article_2795.html https://ijnaa.semnan.ac.ir/article_2795_3990006fa9915eb0af3345e8046f7bc8.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces 293 306 EN Akindele Adebayo Mebawondu School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa dele@aims.ac.za Lateef Jolaoso School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa 216074984@stu.ukzn.ac.za Hammed Abass School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa 216075727@stu.ukzn.ac.za 10.22075/ijnaa.2017.11887.1594 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 https://ijnaa.semnan.ac.ir/article_2799.html https://ijnaa.semnan.ac.ir/article_2799_2ea33223c55fba3700f88bd7aefc3695.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 26 Some common fixed point theorems for four \$(psi,varphi)\$-weakly contractive mappings satisfying rational expressions in ordered partial metric spaces 307 326 EN Rashwan Rashwan Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt rr_rashwan54@yahoo.com S.M. Saleh Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt samirasaleh2007@yahoo.com 10.22075/ijnaa.2016.468 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 https://ijnaa.semnan.ac.ir/article_468.html https://ijnaa.semnan.ac.ir/article_468_a5b9c5cc09ff9b3a978f98266a1b155a.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Mazur-Ulam theorem in probabilistic normed groups 327 333 EN Alireza Pourmoslemi Department of Mathematics, Payame Noor University, Tehran, Iran a_pourmoslemy@pnu.ac.ir Kourosh Nourouzi Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran nourouzi@kntu.ac.ir 10.22075/ijnaa.2017.1281.1318 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 https://ijnaa.semnan.ac.ir/article_2786.html https://ijnaa.semnan.ac.ir/article_2786_313d118769848a5d41636e321e9950d6.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Fixed point theorems for generalized quasi-contractions in cone \$b\$-metric spaces over Banach algebras without the assumption of normality with applications 335 353 EN Shaoyuan Xu School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China xushaoyuan@126.com Suyu Cheng Library, Hanshan Normal University, Chaozhou, 521041, China chengsuyu1992@126.com Suzana Aleksic Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovi\'ca 12, 34000 Kragujevac, Serbia suzanasimic@kg.ac.rs 10.22075/ijnaa.2017.1857.1483 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 https://ijnaa.semnan.ac.ir/article_2787.html https://ijnaa.semnan.ac.ir/article_2787_c82fdf395409faa23840674b2855da21.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 L\$^q\$ inequalities for the \${s^{th}}\$ derivative of a polynomial 355 362 EN Ahmad Zireh Department of Mathematics, Shahrood University of Technology, Shahrood, Iran azireh@gmail.com 10.22075/ijnaa.2017.1286.1321 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 follows<br />begin{align*}<br />begin{split}<br />&left|fright|_q:=left{frac{1}{2pi}int_0^{2pi}left|f(e^{itheta})right|^qdthetaright}^{1/q},<br /> 0<q<infty,\<br />&left|fright|_{infty}:=max_{|z|=1}left|f(z)right|.<br />end{split}<br />end{align*}<br /> 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\$,<br />begin{align*}<br />left|p'right|_{q}leq frac{n}{|k+z|_q}|p|_{q}.<br />end{align*}<br />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 https://ijnaa.semnan.ac.ir/article_2801.html https://ijnaa.semnan.ac.ir/article_2801_1533fb6d1e1801bc30789ab8dc04255b.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 01 Dynamics of higher order rational difference equation \$x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})\$ 363 379 EN Abu Alhalawa Muna Department of Mathematics, Faculty of Science, Birzeit University, Palestine mabualhalawa@birzeit.edu Mohammad Saleh Department of Mathematics, Faculty of Science, Birzeit University, Palestine msaleh@birzeit.edu 10.22075/ijnaa.2017.10822.1526 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<br />\$\$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,\$\$<br />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 https://ijnaa.semnan.ac.ir/article_2794.html https://ijnaa.semnan.ac.ir/article_2794_5faa22d45bfb19c931f7a566b1d51774.pdf