A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function
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
author
Bicheng
Yang
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
1
27
https://ijnaa.semnan.ac.ir/article_375_c8b2e9a805289b56d307b04d2e8cc8c1.pdf
dx.doi.org/10.22075/ijnaa.2016.375
Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition
Somayeh
Saiedinezhad
Assistant professor of Iran University of Science and technology
author
text
article
2016
eng
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$$int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleqCint_0^infty f(x)^{p(x)}u(x)dx,$$ 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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
29
38
https://ijnaa.semnan.ac.ir/article_439_a9ff1b7775e024c726cd0418c812bd7b.pdf
dx.doi.org/10.22075/ijnaa.2016.439
Weak and $(-1)$-weak amenability of second dual of Banach algebras
A.
Valadkhani
University of Simon Fraser, Department of Education, Vancouver, Canada
author
S.A.R.
Hosseinioun
University of Arkansas, Department of Mathematical sciences, Fayetteville, AR 72703, USA
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
39
48
https://ijnaa.semnan.ac.ir/article_457_caf6063aacac36ba84aaec150ac133f2.pdf
dx.doi.org/10.22075/ijnaa.2016.457
Fixed points for Chatterjea contractions on a metric space with a graph
Kamal
Fallahi
Department of Mathematics, Payame Noor University,
P.O. Box 19395-3697, Tehran, Iran
author
Aris
Aghanians
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
49
58
https://ijnaa.semnan.ac.ir/article_449_28e573679a0823fddb453f5c119bc3ee.pdf
dx.doi.org/10.22075/ijnaa.2016.449
Application of new basis functions for solving nonlinear stochastic differential equations
Zahra
Sadati
Department of Mathematics, khomein Branch, Islamic Azad University, khomein, Iran
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
59
68
https://ijnaa.semnan.ac.ir/article_450_5a634288d0d55d50b7448802c0a9f43d.pdf
dx.doi.org/10.22075/ijnaa.2016.450
( p,q)-Genuine Baskakov-Durrmeyer operators
Vijay
Gupta
Netaji Subhas Institute of Technology
New Delhi, India
author
Th.
Rassias
National Technical University of Athens
Department of Mathematics
Zografou Campus,
GR-15780, Athens, Greece
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
69
76
https://ijnaa.semnan.ac.ir/article_454_0436ce511d55e45b51b5f1bf2fc99a3d.pdf
dx.doi.org/10.22075/ijnaa.2016.454
Coincidence point and common fixed point results via scalarization function
Sushanta
Mohanta
West Bengal State University, Barasat, 24 Parganas(North), Kolkata-700126, West Bengal, India
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
77
91
https://ijnaa.semnan.ac.ir/article_478_fcdfd8b1214eedc472509c9cb0d177f6.pdf
dx.doi.org/10.22075/ijnaa.2016.478
Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings
Godwin
Ugwunnadi
Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
93
108
https://ijnaa.semnan.ac.ir/article_479_faac311c75f79ded9e0cb8b61b577217.pdf
dx.doi.org/10.22075/ijnaa.2016.479
Product of derivations on C$^*$-algebras
Khalil
Ekrami
Department of Mathematics, Payame Noor University
author
Madjid
Mirzavaziri
Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Struc-tures (CEAAS), Ferdowsi University of Mashhad
author
Hamid Reza
Ebrahimi Vishki
Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Struc-tures (CEAAS), Ferdowsi University of Mashhad,
author
text
article
2016
eng
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 $s\in\mathbb{C}$.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
109
114
https://ijnaa.semnan.ac.ir/article_451_0bbbe5991acf696ef672151434ad1e2a.pdf
dx.doi.org/10.22075/ijnaa.2017.451
Some drifts on posets and its application to fuzzy subalgebras
Xiaohong
Zhang
College of Arts and Sciences
Shanghai Maritime University
author
Hee Sik
Kim
Research Institute for Natural Sci., Department of Mathematics, Hanyang University, Seoul, 04763, Korea
author
Joseph
Neggers
Department of Mathematics
University of Alabama
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
115
125
https://ijnaa.semnan.ac.ir/article_503_0e526cbeda0c0cac76e960d4f005b888.pdf
dx.doi.org/10.22075/ijnaa.2016.503
The solutions to the operator equation $TXS^* -SX^*T^*=A$ in Hilbert $C^*$-modules
Mehdi
Mohammadzadeh Karizaki
Department of Mathematics,
Mashhad Branch, Islamic Azad University,
Mashhad 91735, Iran
author
Mahmoud
Hassani
Department of Mathematics, Mashhad Branch, Islamic Azad University,
Mashhad, Iran.
author
Dragan
Djordjevic
D. S. Djordjevic, Faculty of Sciences and Mathematics, University of ´
Nis, Visegradska 33, P.O. Box 224, 18000 Nis, Serbia.
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
127
132
https://ijnaa.semnan.ac.ir/article_502_53db64a878b47ab121fa3552645e4306.pdf
dx.doi.org/10.22075/ijnaa.2016.502
Some inequalities in connection to relative orders of entire functions of several complex variables
Sanjib
Datta
Associate Professor
Department of Mathematics
University of Kalyani
author
Tanmay
Biswas
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar, Dist-Nadia,PIN-741101, West Bengal, India
author
Debasmita
Dutta
Mohanpara Nibedita Balika Vidyalaya (High),P.o - Amrity, Block - English Bazar, Dist.- District - Malda, PIN- 732208, West Bengal, India
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
133
141
https://ijnaa.semnan.ac.ir/article_518_df28fc621a27f6e4fc6e1ec5be008124.pdf
dx.doi.org/10.22075/ijnaa.2016.518
A generalization of Martindale's theorem to $(\alpha, \beta)-$homomorphism
Eqbal
Keyhani
Department of Mathematics, Mashhad Branch, Islamic Azad University,
Mashhad, Iran.
author
Mahmoud
Hassani
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
author
Maryam
Amyari
Department of Mathematics, Mashhad Branch, Islamic Azad University,
Mashhad, Iran.
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
143
151
https://ijnaa.semnan.ac.ir/article_481_ad67ee626a0c5ed5b5884900645f4b81.pdf
dx.doi.org/10.22075/ijnaa.2016.481
Algebras defined by homomorphisms
Feysal
Hassani
Payame Noor University
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
153
164
https://ijnaa.semnan.ac.ir/article_456_802d5ab4109a34749b6a7c2c7798aea9.pdf
dx.doi.org/10.22075/ijnaa.2016.456
On boundary value problems of higher order abstract fractional integro-differential equations
Sabri T. M.
Thabet
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University,
Aurangabad - 431004, Maharashtra, India.
author
Machindra B.
Dhakne
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad - 431004, Maharashtra, India.
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
165
184
https://ijnaa.semnan.ac.ir/article_520_194aeb0c75105fe3eb3c003fb975b20e.pdf
dx.doi.org/10.22075/ijnaa.2017.520
Existence of Mild Solutions to a Cauchy Problem Presented by Fractional Evolution Equation with an Integral Initial Condition
Mohamad Hossein
Akrami
Department of Mathematics, Yazd University, Yazd, Iran.
author
Gholam Hussain
Erjaee
Department of Mathematics, College of Science, Shiraz University, 74811-71466 Shiraz, Iran
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
185
193
https://ijnaa.semnan.ac.ir/article_2262_c2b9bd3c99a66a2db8f761f296a64c4b.pdf
dx.doi.org/10.22075/ijnaa.2017.1080.1228
Approximation of a generalized Euler-Lagrange type additive mapping on Lie $C^{\ast}$-algebras
Zhihua
Wang
School of Science, Hubei University of Technology, Wuhan, Hubei 430068, P.R. China
author
Prasanna K.
Sahoo
Department of Mathematics, University of Louisville, Louisville, KY 40292, USA
author
text
article
2016
eng
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 \begin{align*} \sum^{n}_{j=1}f{\bigg(-r_{j}x_{j}+\sum_{1\leq i \leq n, i\neq 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)} \end{align*} where $r_{1},\ldots,r_{n}\in {\mathbb{R}}$ are given and $r_{i},r_{j}\neq 0$ for some $1\leq i< j\leq n$.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
195
204
https://ijnaa.semnan.ac.ir/article_2263_c8c5159b5ec222ee67da73e89bf61592.pdf
dx.doi.org/10.22075/ijnaa.2017.1332.1329
Existence of solutions of infinite systems of integral equations in the Frechet spaces
Reza
Arab
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
author
Reza
Allahyari
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
author
Ali
Shole Haghighi
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
205
216
https://ijnaa.semnan.ac.ir/article_2264_d473862b05d2a18a6a30b75788356ff0.pdf
dx.doi.org/10.22075/ijnaa.2017.1074.1222
Some common fixed point theorems for Gregus type mappings
Sumit
Chandok
School of Mathematics, Thapar University, Patiala-147004, Punjab, India
author
text
article
2016
eng
In this paper, sufficient conditions for the existence of common fixed points for a compatible pair of self maps of Gregustype 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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
217
228
https://ijnaa.semnan.ac.ir/article_2272_ae88375151c0dfb6fc680b0a1f00781f.pdf
dx.doi.org/10.22075/ijnaa.2017.10452.1504
A contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies
John
Venetis
School of Applied Mathematics and Physical Sciences NTUA, Section of Mechanics, 5 Heroes of Polytechnion Avenue GR,15773 Athens, Greece
author
Emilios
Sideridis
School of Applied Mathematics and Physical Sciences NTUA, Section of Mechanics, 5 Heroes of Polytechnion Avenue GR,15773 Athens, Greece.
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
229
242
https://ijnaa.semnan.ac.ir/article_2308_89fe59563da22b632b56d4c4ff3a0620.pdf
dx.doi.org/10.22075/ijnaa.2017.10573.1510
Projected non-stationary simultaneous iterative methods
Touraj
Nikazad
School of Mathematics,
Iran University of Science and Technology
author
Mahdi
Mirzapour
School of Mathematics,
Iran University of Science and Technology
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
243
251
https://ijnaa.semnan.ac.ir/article_501_d9a27af16a0f373c8ccda25b95136ec7.pdf
dx.doi.org/10.22075/ijnaa.2016.501
Random fractional functional differential equations
Vu
Ho
Institute for Computational Science
Ton Duc Thang University;
19 Nguyen Huu Tho, District 7, Ho Chi Minh City, Vietnam
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
253
267
https://ijnaa.semnan.ac.ir/article_2309_3b8da04d29148ca35bf85766e16ab224.pdf
dx.doi.org/10.22075/ijnaa.2017.980.1185
Differential transform method for a a nonlinear system of differential equations arising in HIV infection of CD4+T cell
Javad
Damirchi
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University,Semnan, Iran
author
Taher
Rahimi shamami
Department of Mathematics, Faculsty of Mathematics, Statistics and Computer Science, Semnan University, Semnan Iran
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
269
277
https://ijnaa.semnan.ac.ir/article_458_eb4989c1d76da877a5c06a66b8d994fd.pdf
dx.doi.org/10.22075/ijnaa.2016.458
Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations
Th.M.
Rassias
Department of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, Greece
author
Elhoucien
Elqorachi
Ibn Zohr University, Faculty of Sciences
Department of Mathematic, Agadir, Morocco
author
Ahmed
Redouani
Ibn Zohr University, Faculty of Sciences
Department of Mathematic, Agadir, Morocco
author
text
article
2016
eng
In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$\int_{S}f(\sigma(y)xt)d\mu(t)-\int_{S}f(xyt)d\mu(t) = 2f(x)f(y), \;x,y\in S,$$ 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 $$\int_{S}f(xty)d\upsilon(t)+\int_{S}f(\sigma(y)tx)d\upsilon(t) = 2f(x)f(y), \;x,y\in S,$$ 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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
279
301
https://ijnaa.semnan.ac.ir/article_774_ac5ba88e6d8ed3f180cc2ff75a074111.pdf
dx.doi.org/10.22075/ijnaa.2017.1803.1472
Fractional dynamical systems: A fresh view on the local qualitative theorems
Khosro
Sayevand
Faculty of Mathematical Sciences, Malayer University, P.O.Box 16846-13114, Malayer, Iran
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
303
318
https://ijnaa.semnan.ac.ir/article_505_6dd6f750a1f5b7ac40e8c8f4e08ab830.pdf
dx.doi.org/10.22075/ijnaa.2016.505
Asymptotic behavior of a system of two difference equations of exponential form
Mai Nam
Phong
Department of Mathematical Analysis, University of Transport and Communications, Hanoi City, Vietnam
author
Vu Van
Khuong
Department of Mathematical Analysis, University of Transport and Communications, Hanoi City, Vietnam
author
text
article
2016
eng
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: \begin{equation*} 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} \end{equation*} where $a,\ b,\ c,\ d$ are positive constants and the initial values $ x_0,\ y_0$ are positive real values.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
319
329
https://ijnaa.semnan.ac.ir/article_2317_fd9ef87284cd65c4c0051d2f2524b18c.pdf
dx.doi.org/10.22075/ijnaa.2017.1301.1320
A numerical scheme for space-time fractional advection-dispersion equation
Shahnam
Javadi
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University
author
Mostafa
Jani
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
author
Esmail
Babolian
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
331
343
https://ijnaa.semnan.ac.ir/article_2319_26e1ee558045f8ddff548d3f3b47e268.pdf
dx.doi.org/10.22075/ijnaa.2017.1129.1249
On some generalisations of Brown's conjecture
Bashir Ahmad
Zargar
Department of Mathematics, University of Kashmir, Hazratbal, Srinagar
author
Manzoor
Ahmad
Department of Mathematics, University of Kashmir, Hazratbal, Srinagar
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
345
349
https://ijnaa.semnan.ac.ir/article_2320_2cb9da095415c881426e1ad3495e119c.pdf
dx.doi.org/10.22075/ijnaa.2016.2320
Existence of three solutions for a class of fractional boundary value systems
Samad
Mohseni Kolagar
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
author
Ghasem A.
Afrouzi
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
author
Armin
Hadjian
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
351
362
https://ijnaa.semnan.ac.ir/article_2321_5863ebd05baaf26bc703c4dde8cca5ba.pdf
dx.doi.org/10.22075/ijnaa.2017.1241.1296
On best proximity points for multivalued cyclic $F$-contraction mappings
Konrawut
Khammahawong
King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
author
Parinya
Sa Ngiamsunthorn
Department of Mathematics,
Faculty of Science,
King Mongkut’s University of Technology Thonburi (KMUTT),
126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand.
author
Poom
Kumam
King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
author
text
article
2016
eng
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.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
2
no.
2016
363
374
https://ijnaa.semnan.ac.ir/article_2322_a14950d6213380e677cbc576639e0d60.pdf
dx.doi.org/10.22075/ijnaa.2017.2322