Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function 1 27 375 10.22075/ijnaa.2016.375 EN Michael Th. Rassias Institute of Mathematics, University of Zurich, CH-8057, Zurich, Switzerland \ & Institute for Advanced Study, Program in Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ 08540, USA Bicheng Yang Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China Journal Article 2015 05 11 By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the reverses and some particular cases are also considered. Hardy-Hilbert-type inequality extended Riemann-zeta function Hurwitz zeta function Gamma function weight function equivalent form operator https://ijnaa.semnan.ac.ir/article_375_c8b2e9a805289b56d307b04d2e8cc8c1.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition 29 38 439 10.22075/ijnaa.2016.439 EN Somayeh Saiedinezhad Assistant professor of Iran University of Science and technology Journal Article 2015 12 05 ‎Some functional inequalities‎ ‎in variable exponent Lebesgue spaces are presented‎. ‎The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non‎- ‎increasing function which is‎<br />‎$$‎<br />‎int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq‎<br />‎Cint_0^infty f(x)^{p(x)}u(x)dx‎,<br />‎$$‎<br />‎is studied‎. ‎We show that the exponent $p(.)$ for which these modular inequalities hold must have constant oscillation‎. ‎Also we study the boundedness of integral operator $Tf(x)=int K(x,y) f(x)dy$ on $L^{p(.)}$ when the variable exponent $p(.)$ satisfies some‎ ‎uniform continuity condition that is named $beta$-controller condition and so multiple interesting results which can be‎ ‎seen as a generalization of the same classical results in the constant exponent case‎, ‎derived‎. Hardy type inequality Variable exponent Lebesgue space Modular type inequality.‎ https://ijnaa.semnan.ac.ir/article_439_a9ff1b7775e024c726cd0418c812bd7b.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Weak and $(-1)$-weak amenability of second dual of Banach algebras 39 48 457 10.22075/ijnaa.2016.457 EN A. Valadkhani University of Simon Fraser, Department of Education, Vancouver, Canada S.A.R. Hosseinioun University of Arkansas, Department of Mathematical sciences, Fayetteville, AR 72703, USA Journal Article 2015 12 19 For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')=\{0\}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^\ast$-algebra is $(-1)$-Weakly amenable. Banach algebra point derivation (-1)-Weak amenability https://ijnaa.semnan.ac.ir/article_457_caf6063aacac36ba84aaec150ac133f2.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Fixed points for Chatterjea contractions on a metric space with a graph 49 58 449 10.22075/ijnaa.2016.449 EN Kamal Fallahi Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran Aris Aghanians Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran Journal Article 2014 12 23 In this work‎, ‎we formulate Chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. We also discuss the uniqueness of the fixed point. The given result is a generalization of Chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a graph. ‎$‎G‎$‎-Chatterjea mapping Fixed point orbitally ‎$‎G‎$‎-continuous mapping https://ijnaa.semnan.ac.ir/article_449_28e573679a0823fddb453f5c119bc3ee.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Application of new basis functions for solving nonlinear stochastic differential equations 59 68 450 10.22075/ijnaa.2016.450 EN Zahra Sadati Department of Mathematics, khomein Branch, Islamic Azad University, khomein, Iran Journal Article 2014 05 19 This paper presents an approach for solving a nonlinear stochastic differential equations (NSDEs) using a new basis functions (NBFs). These functions and their operational matrices are used for representing matrix form of the NBFs. With using this method in combination with the collocation method, the NSDEs are reduced a stochastic nonlinear system of equations and unknowns. Then, the error analysis is proved. Finally, numerical examples illustrate applicability and accuracy of the presented method. New basis functions Standard Brownian motion Stochastic operational matrix Nonlinear stochastic differential equations https://ijnaa.semnan.ac.ir/article_450_5a634288d0d55d50b7448802c0a9f43d.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 ( p,q)-Genuine Baskakov-Durrmeyer operators 69 76 454 10.22075/ijnaa.2016.454 EN Vijay Gupta Netaji Subhas Institute of Technology New Delhi, India Th. M. Rassias National Technical University of Athens Department of Mathematics Zografou Campus, GR-15780, Athens, Greece Journal Article 2015 12 18 In the present article, we propose the $(p,q)$ variant of genuine Baskakov Durrmeyer operators. We obtain moments and establish some direct results, which include weighted approximation and results in terms of modulus of continuity of second order. q)$-Beta function $(p q)$-Gamma function Baskakov operators Durrmeyer variant Steklov mean $K$-functional direct estimates https://ijnaa.semnan.ac.ir/article_454_0436ce511d55e45b51b5f1bf2fc99a3d.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Coincidence point and common fixed point results via scalarization function 77 91 478 10.22075/ijnaa.2016.478 EN Sushanta Mohanta West Bengal State University, Barasat, 24 Parganas(North), Kolkata-700126, West Bengal, India Journal Article 2014 08 09 The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for three self mappings in $b$-metric spaces. Next, we obtain cone $b$-metric version of these results by using a scalarization function. Our results extend and generalize several well known comparable results in the existing literature. Cone $b$-metric space scalarization function point of coincidence Common fixed point https://ijnaa.semnan.ac.ir/article_478_fcdfd8b1214eedc472509c9cb0d177f6.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings 93 108 479 10.22075/ijnaa.2016.479 EN Godwin Chidi Ugwunnadi Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria Journal Article 2014 08 24 In this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real reflexive Banach space  with a uniformly G$\hat{a}$teaux differentiable norm. Our result is applicable in $L_{p}(\ell_{p})$ spaces, $1 < p <\infty$ and consequently in sobolev spaces. Fixed point Banach space Asymptotically nonexpansive mapping https://ijnaa.semnan.ac.ir/article_479_faac311c75f79ded9e0cb8b61b577217.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Product of derivations on C$^*$-algebras 109 114 451 10.22075/ijnaa.2017.451 EN Khalil Ekrami Department of Mathematics, Payame Noor University Madjid Mirzavaziri Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Struc-tures (CEAAS), Ferdowsi University of Mashhad Hamid Reza Ebrahimi Vishki Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Struc-tures (CEAAS), Ferdowsi University of Mashhad, Journal Article 2016 07 17 Let $\mathfrak{A}$ be an algebra. A linear mapping $\delta:\mathfrak{A}\to\mathfrak{A}$ is called a \textit{derivation} if $\delta(ab)=\delta(a)b+a\delta(b)$ for each $a,b\in\mathfrak{A}$. Given two derivations $\delta$ and $\delta'$ on a $C^*$-algebra $\mathfrak A$, we prove that there exists a derivation $\Delta$ on $\mathfrak A$ such that $\delta\delta'=\Delta^2$ if and only if either $\delta'=0$ or $\delta=s\delta'$ for some $s\in\mathbb{C}$. Derivation C$^*$-algebra https://ijnaa.semnan.ac.ir/article_451_0bbbe5991acf696ef672151434ad1e2a.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Some drifts on posets and its application to fuzzy subalgebras 115 125 503 10.22075/ijnaa.2016.503 EN Xiaohong Zhang College of Arts and Sciences Shanghai Maritime University, China Hee Sik Kim Research Institute for Natural Sci., Department of Mathematics, Hanyang University, Seoul, 04763, Korea Joseph Neggers Department of Mathematics University of Alabama, USA Journal Article 2015 12 18 In this paper, given a poset $(X,\leq)$, we introduce some  drifts on a groupoid $(X,*)$ with respect to $(X,\leq)$, and we obtain several properties of these drifts related to the notion of $Bin(X)$. We discuss some connections between fuzzy subalgebras and upward drifts. $Bin(X)$ (strong oriented positive strict) upward drift selective $BCK$-algebra fuzzy subalgebra https://ijnaa.semnan.ac.ir/article_503_0e526cbeda0c0cac76e960d4f005b888.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 The solutions to the operator equation $TXS^* -SX^*T^*=A$ in Hilbert $C^*$-modules 127 132 502 10.22075/ijnaa.2016.502 EN Mehdi Mohammadzadeh Karizaki Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad 91735, Iran Mahmoud Hassani Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. Dragan Djordjevic D. S. Djordjevic, Faculty of Sciences and Mathematics, University of acute; Nis, Visegradska 33, P.O. Box 224, 18000 Nis, Serbia. Journal Article 2015 11 19 In this paper, we find explicit solution to the operator equation $TXS^* -SX^*T^*=A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $T,S$ have closed ranges and $S$ is a self adjoint operator. Operator equation Moore-Penrose inverse Hilbert $C^*$-module https://ijnaa.semnan.ac.ir/article_502_53db64a878b47ab121fa3552645e4306.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Some inequalities in connection to relative orders of entire functions of several complex variables 133 141 518 10.22075/ijnaa.2016.518 EN Sanjib Kumar Datta Associate Professor Department of Mathematics University of Kalyani Tanmay Biswas Rajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar, Dist-Nadia,PIN-741101, West Bengal, India Debasmita Dutta Mohanpara Nibedita Balika Vidyalaya (High),P.o - Amrity, Block - English Bazar, Dist.- District - Malda, PIN- 732208, West Bengal, India Journal Article 2015 07 12 Let f, g and h be all entire functions of several complex variables. In this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given. Entire function several complex variables relative order relative lower order https://ijnaa.semnan.ac.ir/article_518_df28fc621a27f6e4fc6e1ec5be008124.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 A generalization of Martindale's theorem to $(\alpha, \beta)-$homomorphism 143 151 481 10.22075/ijnaa.2016.481 EN Eqbal Keyhani Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. Mahmoud Hassani Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran Maryam Amyari Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. Journal Article 2015 01 16 Martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. In this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(\alpha, \beta)-$derivation is additive. beta)-$multiplicative mapping beta)-$multiplicative isomorphism $(alpha beta)-$additive mapping multiplicative $(alpha beta)-$derivations https://ijnaa.semnan.ac.ir/article_481_ad67ee626a0c5ed5b5884900645f4b81.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Algebras defined by homomorphisms 153 164 456 10.22075/ijnaa.2016.456 EN Feysal Hassani Payame Noor University Journal Article 2016 09 15 Let $\mathcal{R}$ be a  commutative ring with identity, let $A$ and $B$ be two $\mathcal{R}$-algebras and $\varphi:B\longrightarrow A$ be an $\mathcal{R}$-additive algebra homomorphism. We introduce a new algebra $A\times_\varphi B$, and give some basic properties of this algebra. Generalized $2$-cocycle derivations on $A\times_\varphi B$ are studied. Accordingly, $A\times_\varphi B$ is considered from the perspective of Banach algebras. algebra cocycle generalized derivation Banach algebra https://ijnaa.semnan.ac.ir/article_456_802d5ab4109a34749b6a7c2c7798aea9.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 On boundary value problems of higher order abstract fractional integro-differential equations 165 184 520 10.22075/ijnaa.2017.520 EN Sabri T. M. Thabet Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad - 431004, Maharashtra, India. Machindra B. Dhakne Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad - 431004, Maharashtra, India. Journal Article 2015 08 25 The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H\"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main results. Fractional integro-differential equations boundary value problem fixed point theorems https://ijnaa.semnan.ac.ir/article_520_194aeb0c75105fe3eb3c003fb975b20e.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Existence of Mild Solutions to a Cauchy Problem Presented by Fractional Evolution Equation with an Integral Initial Condition 185 193 2262 10.22075/ijnaa.2017.1080.1228 EN Mohamad Hossein Akrami Department of Mathematics, Yazd University, Yazd, Iran. Gholam Hussain Erjaee Department of Mathematics, College of Science, Shiraz University, 74811-71466 Shiraz, Iran Journal Article 2015 12 21 In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces. Fractional evolution equation Cauchy problem Fixed point theorem Mild solution https://ijnaa.semnan.ac.ir/article_2262_c2b9bd3c99a66a2db8f761f296a64c4b.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Approximation of a generalized Euler-Lagrange type additive mapping on Lie $C^{\ast}$-algebras 195 204 2263 10.22075/ijnaa.2017.1332.1329 EN Zhihua Wang School of Science, Hubei University of Technology, Wuhan, Hubei 430068, P.R. China Prasanna K. Sahoo Department of Mathematics, University of Louisville, Louisville, KY 40292, USA Journal Article 2016 04 17 Using fixed point method, we prove some new stability results for Lie $(\alpha,\beta,\gamma)$-derivations and Lie $C^{\ast}$-algebra homomorphisms on Lie $C^{\ast}$-algebras associated with the Euler-Lagrange type additive functional equation<br />\begin{align*}<br />\sum^{n}_{j=1}f{\bigg(-r_{j}x_{j}+\sum_{1\leq i \leq n, i\neq<br />j}r_{i}x_{i}\bigg)}+2\sum^{n}_{i=1}r_{i}f(x_{i})=nf{\bigg(\sum^{n}_{i=1}r_{i}x_{i}\bigg)}<br />\end{align*}<br />where $r_{1},\ldots,r_{n}\in {\mathbb{R}}$ are given and $r_{i},r_{j}\neq 0$ for some $1\leq i< j\leq n$. Fixed point theorem Lie $(alpha,beta,gamma)$-derivation Lie $C^{ast}$-algebra homomorphisms generalized Hyers-Ulam stability https://ijnaa.semnan.ac.ir/article_2263_c8c5159b5ec222ee67da73e89bf61592.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Existence of solutions of infinite systems of integral equations in the Frechet spaces 205 216 2264 10.22075/ijnaa.2017.1074.1222 EN Reza Arab Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran Reza Allahyari Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. Ali Shole Haghighi Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran. Journal Article 2015 12 19 In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tychonoff fixed point theorem. Also, we present an example of nonlinear integral equations to show the efficiency of our results. Our results extend several comparable results obtained in the previous literature. Measure of noncompactness Frechet space Tychonoff fixed point theorem Infinite systems of equations https://ijnaa.semnan.ac.ir/article_2264_d473862b05d2a18a6a30b75788356ff0.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Some common fixed point theorems for Gregus type mappings 217 228 2272 10.22075/ijnaa.2017.10452.1504 EN Sumit Chandok School of Mathematics, Thapar University, Patiala-147004, Punjab, India Journal Article 2014 08 03 In this paper, sufficient conditions for the existence of common fixed points for a compatible pair of self maps of Gregus<br />type in the framework of convex metric spaces have been obtained. Also, established the existence of common fixed points for a pair of compatible mappings of type (B) and consequently for compatible mappings of type (A). The proved results generalize and extend some of the well known results of the literature. Common fixed point convex set commuting maps compatible maps compatible maps of type (A) compatible maps of type (B) affine map https://ijnaa.semnan.ac.ir/article_2272_ae88375151c0dfb6fc680b0a1f00781f.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 A contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies 229 242 2308 10.22075/ijnaa.2017.10573.1510 EN John Venetis School of Applied Mathematics and Physical Sciences NTUA, Section of Mechanics, 5 Heroes of Polytechnion Avenue GR,15773 Athens, Greece Emilios Sideridis School of Applied Mathematics and Physical Sciences NTUA, Section of Mechanics, 5 Heroes of Polytechnion Avenue GR,15773 Athens, Greece. Journal Article 2014 02 12 In the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. The basic assumption is that the class of functions that we investigate here, except the verification of Dirichlet's principles, is concurrently able to be expanded in Taylor's representation, over a particular interval of their domain of definition. Thus, we shall take into account the simultaneous validity of these two properties over this interval, in order to obtain an alternative equivalent representation of the corresponding harmonic decomposition for this category of functions. In the sequel, we shall also implement this resultant formula in the investigation of turbulence spectrum of eddies according to known from literature Von Karman's formulation, making the additional assumption that during the evolution of such stochastic dynamic effects with respect to time, the occasional time-returning period can be actually supposed to tend to infinity. Orthogonal functions Abel's summability Poisson's kernel Von Karman's spectrum https://ijnaa.semnan.ac.ir/article_2308_89fe59563da22b632b56d4c4ff3a0620.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Projected non-stationary simultaneous iterative methods 243 251 501 10.22075/ijnaa.2016.501 EN Touraj Nikazad School of Mathematics, Iran University of Science and Technology Mahdi Mirzapour School of Mathematics, Iran University of Science and Technology Journal Article 2015 10 08 In this paper, we study Projected non-stationary Simultaneous It-erative Reconstruction Techniques (P-SIRT). Based on algorithmic op-erators, convergence result are adjusted with Opial’s Theorem. The advantages of P-SIRT are demonstrated on examples taken from to-mographic imaging. Simultaneous iterative reconstruction techniques convex feasibility problem (firmly) nonexpansive operator cutter operator https://ijnaa.semnan.ac.ir/article_501_d9a27af16a0f373c8ccda25b95136ec7.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Random fractional functional differential equations 253 267 2309 10.22075/ijnaa.2017.980.1185 EN Vu Ho Institute for Computational Science Ton Duc Thang University; 19 Nguyen Huu Tho, District 7, Ho Chi Minh City, Vietnam Journal Article 2015 10 28 In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered. Sample fractional integral Sample fractional derivative Fractional differential equations random differential equations Caputo fractional derivative https://ijnaa.semnan.ac.ir/article_2309_3b8da04d29148ca35bf85766e16ab224.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Differential transform method for a a nonlinear system of differential equations arising in HIV infection of CD4+T cell 269 277 458 10.22075/ijnaa.2016.458 EN Javad Damirchi Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University,Semnan, Iran Taher Rahimi Shamami Department of Mathematics, Faculsty of Mathematics, Statistics and Computer Science, Semnan University, Semnan Iran Journal Article 2016 01 02 In this paper, differential transform method (DTM) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in HIV infections of cell. Intervals of validity of the solution will be extended by using Pade approximation. The results also will be compared with those results obtained by Runge-Kutta method. The technique is described and is illustrated with one numerical example. The numerical results shown that the reliability and efficiency of the method. Differential transform method Systems of nonlinear ordinary differential equations Pade approximation Fourth order Runge-Kutta method https://ijnaa.semnan.ac.ir/article_458_eb4989c1d76da877a5c06a66b8d994fd.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations 279 301 774 10.22075/ijnaa.2017.1803.1472 EN Th.M. Rassias Department of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, Greece Elhoucien Elqorachi Ibn Zohr University, Faculty of Sciences Department of Mathematic, Agadir, Morocco Ahmed Redouani Ibn Zohr University, Faculty of Sciences Department of Mathematic, Agadir, Morocco Journal Article 2015 12 20 In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation<br />$$\int_{S}f(\sigma(y)xt)d\mu(t)-\int_{S}f(xyt)d\mu(t) = 2f(x)f(y), \;x,y\in S,$$ where $S$ is a semigroup, $\sigma$ is an involutive morphism of $S$, and $\mu$ is a complex measure that is linear combinations of Dirac measures $(\delta_{z_{i}})_{i\in I}$, such that for all $i\in I$, $z_{i}$ is contained in the center of $S$. (2) We determine the complex-valued continuous solutions of the following variant of d'Alembert's functional equation<br />$$\int_{S}f(xty)d\upsilon(t)+\int_{S}f(\sigma(y)tx)d\upsilon(t) = 2f(x)f(y), \;x,y\in S,$$ where $S$ is a topological semigroup, $\sigma$ is a continuous involutive automorphism of $S$, and $\upsilon$ is a complex measure with compact support and which is $\sigma$-invariant. (3) We prove the superstability theorems of the first functional equation. semigroup d'Alembert's equation Van Vleck's equation, sine function involution multiplicative function, homomorphism, superstability https://ijnaa.semnan.ac.ir/article_774_ac5ba88e6d8ed3f180cc2ff75a074111.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Fractional dynamical systems: A fresh view on the local qualitative theorems 303 318 505 10.22075/ijnaa.2016.505 EN Khosro Sayevand Faculty of Mathematical Sciences, Malayer University, P.O.Box 16846-13114, Malayer, Iran Journal Article 2016 02 05 The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of the local center manifold theorem, the stable manifold theorem and the Hartman-Grobman theorem to the scope of fractional differential systems. These latter two theorems establish that the qualitative behavior of the solution set of a nonlinear system of fractional differential equations near an equilibrium point is typically the same as the qualitative behavior of the solution set of the corresponding linearized system near the equilibrium point. Furthermore, we discuss the stability conditions for the equilibrium points of these systems. We point out that, the fractional derivative in these systems is in the Caputo sense. Fractional differential systems Stable manifold theorem Hartman-Grobman theorem Local center manifold theorem Local qualitative theory https://ijnaa.semnan.ac.ir/article_505_6dd6f750a1f5b7ac40e8c8f4e08ab830.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Asymptotic behavior of a system of two difference equations of exponential form 319 329 2317 10.22075/ijnaa.2017.1301.1320 EN Mai Nam Phong Department of Mathematical Analysis, University of Transport and Communications, Hanoi City, Vietnam Vu Van Khuong Department of Mathematical Analysis, University of Transport and Communications, Hanoi City, Vietnam Journal Article 2016 03 31 In this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $E=(\bar{x},\ \bar{y})$ of the system of two difference equations of exponential form:<br />\begin{equation*}<br />x_{n+1}=\dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n},\ y_{n+1}=\dfrac{a+e^{-(by_n+cx_n)}}{d+by_n+cx_n}<br />\end{equation*}<br />where $a,\ b,\ c,\ d$ are positive constants and the initial values $ x_0,\ y_0$ are positive real values. Difference equations boundedness persistence asymptotic behavior rate of convergence https://ijnaa.semnan.ac.ir/article_2317_fd9ef87284cd65c4c0051d2f2524b18c.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 A numerical scheme for space-time fractional advection-dispersion equation 331 343 2319 10.22075/ijnaa.2017.1129.1249 EN Shahnam Javadi Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University Mostafa Jani Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran Esmail Babolian Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran Journal Article 2016 01 12 In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed into a linear system of algebraic equations. Matrix formulation, error analysis and order of convergence of the proposed method are also discussed. Some numerical experiments are presented to demonstrate the effectiveness of the proposed method and to confirm the analytic results. Advection-dispersion equation Space-time fractional PDE Bernstein polynomials Product integration Spectral-collocation https://ijnaa.semnan.ac.ir/article_2319_26e1ee558045f8ddff548d3f3b47e268.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 On some generalisations of Brown's conjecture 345 349 2320 10.22075/ijnaa.2016.2320 EN Bashir Ahmad Zargar Department of Mathematics, University of Kashmir, Hazratbal, Srinagar, India Manzoor Ahmad Department of Mathematics, University of Kashmir, Hazratbal, Srinagar, India Journal Article 2015 02 26 Let $P$ be a complex polynomial of the form $P(z)=z\displaystyle\prod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|\ge 1,1\le k\le n-1$ then $ P^\prime(z)\ne 0$. If $|z|<\dfrac {1}{n}$. In this paper, we present some interesting generalisations of this result. Critical points Sendove's Conjecture Coincidence theorem of walsh https://ijnaa.semnan.ac.ir/article_2320_2cb9da095415c881426e1ad3495e119c.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 Existence of three solutions for a class of fractional boundary value systems 351 362 2321 10.22075/ijnaa.2017.1241.1296 EN Samad Mohseni Kolagar Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran Ghasem A. Afrouzi Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran Armin Hadjian Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran Journal Article 2016 03 01 In this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. These problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive Banach space. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. We also give an example to illustrate the obtained result. Fractional differential equations Riemann-Liouville fractional derivatives Variational methods Three solutions https://ijnaa.semnan.ac.ir/article_2321_5863ebd05baaf26bc703c4dde8cca5ba.pdf
Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 2 2016 12 20 On best proximity points for multivalued cyclic $F$-contraction mappings 363 374 2322 10.22075/ijnaa.2017.2322 EN Konrawut Khammahawong King Mongkut&#039;s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand Parinya Sa Ngiamsunthorn Department of Mathematics, Faculty of Science, King Mongkut&rsquo;s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand. Poom Kumam King Mongkut&#039;s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand Journal Article 2016 06 05 In this paper, we establish and prove the existence of best proximity points for multivalued cyclic $F$- contraction mappings in complete metric spaces. Our results improve and extend various results in literature. best proximity point cyclic contraction $F$-contraction multivalued mapping metric space https://ijnaa.semnan.ac.ir/article_2322_a14950d6213380e677cbc576639e0d60.pdf