eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-06-01
7
2
1
27
10.22075/ijnaa.2016.375
375
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
michail.rassias@math.uzh.ch
1
Bicheng Yang
bcyang@gdei.edu.cn
2
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
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
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.
https://ijnaa.semnan.ac.ir/article_375_c8b2e9a805289b56d307b04d2e8cc8c1.pdf
Hardy-Hilbert-type inequality
extended Riemann-zeta function
Hurwitz zeta function
Gamma function
weight function
equivalent form
operator
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-07-01
7
2
29
38
10.22075/ijnaa.2016.439
439
Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition
Somayeh Saiedinezhad
ssaiedinezhad@iust.ac.ir
1
Assistant professor of Iran University of Science and technology
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.
https://ijnaa.semnan.ac.ir/article_439_a9ff1b7775e024c726cd0418c812bd7b.pdf
Hardy type inequality
Variable exponent Lebesgue space
Modular type inequality.
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-06-01
7
2
39
48
10.22075/ijnaa.2016.457
457
Weak and $(-1)$-weak amenability of second dual of Banach algebras
A. Valadkhani
arezou.valadkhani@yahoo.com
1
S.A.R. Hosseinioun
ahosseinioun@yahoo.com
2
University of Simon Fraser, Department of Education, Vancouver, Canada
University of Arkansas, Department of Mathematical sciences, Fayetteville, AR 72703, USA
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.
https://ijnaa.semnan.ac.ir/article_457_caf6063aacac36ba84aaec150ac133f2.pdf
Banach algebra
point derivation
(-1)-Weak amenability
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-05-05
7
2
49
58
10.22075/ijnaa.2016.449
449
Fixed points for Chatterjea contractions on a metric space with a graph
Kamal Fallahi
fallahi1361@gmail.com
1
Aris Aghanians
a.aghanians@dena.kntu.ac.ir
2
Department of Mathematics, Payame Noor University,
P.O. Box 19395-3697, Tehran, Iran
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran
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.
https://ijnaa.semnan.ac.ir/article_449_28e573679a0823fddb453f5c119bc3ee.pdf
$G$-Chatterjea mapping
Fixed point
orbitally $G$-continuous mapping
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-09-09
7
2
59
68
10.22075/ijnaa.2016.450
450
Application of new basis functions for solving nonlinear stochastic differential equations
Zahra Sadati
zahra_sadati47@yahoo.com
1
Department of Mathematics, khomein Branch, Islamic Azad University, khomein, Iran
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.
https://ijnaa.semnan.ac.ir/article_450_5a634288d0d55d50b7448802c0a9f43d.pdf
New basis functions
Standard Brownian motion
Stochastic operational matrix
Nonlinear stochastic differential equations
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-07-01
7
2
69
76
10.22075/ijnaa.2016.454
454
( p,q)-Genuine Baskakov-Durrmeyer operators
Vijay Gupta
vijaygupta2001@hotmail.com
1
Th. Rassias
trassias@math.ntua.gr
2
Netaji Subhas Institute of Technology
New Delhi, India
National Technical University of Athens Department of Mathematics Zografou Campus, GR-15780, Athens, Greece
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.
https://ijnaa.semnan.ac.ir/article_454_0436ce511d55e45b51b5f1bf2fc99a3d.pdf
q)$-Beta function
$(p
q)$-Gamma function
Baskakov operators
Durrmeyer variant
Steklov mean
$K$-functional
direct estimates
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-06-12
7
2
77
91
10.22075/ijnaa.2016.478
478
Coincidence point and common fixed point results via scalarization function
Sushanta Mohanta
mohantawbsu@rediffmail.com
1
West Bengal State University, Barasat, 24 Parganas(North), Kolkata-700126, West Bengal, India
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.
https://ijnaa.semnan.ac.ir/article_478_fcdfd8b1214eedc472509c9cb0d177f6.pdf
Cone $b$-metric space
scalarization function
point of coincidence
Common fixed point
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-08-06
7
2
93
108
10.22075/ijnaa.2016.479
479
Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings
Godwin Ugwunnadi
ugwunnadi4u@yahoo.com
1
Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria
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.
https://ijnaa.semnan.ac.ir/article_479_faac311c75f79ded9e0cb8b61b577217.pdf
Fixed point
Banach space
Asymptotically nonexpansive mapping
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-30
7
2
109
114
10.22075/ijnaa.2017.451
451
Product of derivations on C$^*$-algebras
Khalil Ekrami
khalil.ekrami@gmail.com
1
Madjid Mirzavaziri
mirzavaziri@gmail.com
2
Hamid Reza Ebrahimi Vishki
vishki@um.ac.ir
3
Department of Mathematics, Payame Noor University
Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Struc-tures (CEAAS), Ferdowsi University of Mashhad
Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Struc-tures (CEAAS), Ferdowsi University of Mashhad,
Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. 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 $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdelta'$ for some $sinmathbb{C}$.
https://ijnaa.semnan.ac.ir/article_451_0bbbe5991acf696ef672151434ad1e2a.pdf
Derivation
C$^*$-algebra
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-01
7
2
115
125
10.22075/ijnaa.2016.503
503
Some drifts on posets and its application to fuzzy subalgebras
Xiaohong Zhang
zxhongz@263.net
1
Hee Sik Kim
heekim@hanyang.ac.kr
2
Joseph Neggers
jneggers@as.ua.edu
3
College of Arts and Sciences Shanghai Maritime University
Research Institute for Natural Sci., Department of Mathematics, Hanyang University, Seoul, 04763, Korea
Department of Mathematics University of Alabama
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.
https://ijnaa.semnan.ac.ir/article_503_0e526cbeda0c0cac76e960d4f005b888.pdf
$Bin(X)$
(strong
oriented
positive
strict) upward drift
selective
$BCK$-algebra
fuzzy subalgebra
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-11-14
7
2
127
132
10.22075/ijnaa.2016.502
502
The solutions to the operator equation $TXS^* -SX^*T^*=A$ in Hilbert $C^*$-modules
Mehdi Mohammadzadeh Karizaki
mohammadzadehkarizaki@gmail.com
1
Mahmoud Hassani
mhassanimath@gmail.com
2
Dragan Djordjevic
dragan@pmf.ni.ac.rs
3
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad 91735, Iran
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
D. S. Djordjevic, Faculty of Sciences and Mathematics, University of ´ Nis, Visegradska 33, P.O. Box 224, 18000 Nis, Serbia.
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.
https://ijnaa.semnan.ac.ir/article_502_53db64a878b47ab121fa3552645e4306.pdf
Operator equation
Moore-Penrose inverse
Hilbert $C^*$-module
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-03
7
2
133
141
10.22075/ijnaa.2016.518
518
Some inequalities in connection to relative orders of entire functions of several complex variables
Sanjib Datta
sanjib_kr_datta@yahoo.co.in
1
Tanmay Biswas
tanmaybiswas_math@rediffmail.com
2
Debasmita Dutta
debasmita.dut@gmail.com
3
Associate Professor
Department of Mathematics
University of Kalyani
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar, Dist-Nadia,PIN-741101, West Bengal, India
Mohanpara Nibedita Balika Vidyalaya (High),P.o - Amrity, Block - English Bazar, Dist.- District - Malda, PIN- 732208, West Bengal, India
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.
https://ijnaa.semnan.ac.ir/article_518_df28fc621a27f6e4fc6e1ec5be008124.pdf
Entire function
several complex variables
relative order
relative lower order
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-06-01
7
2
143
151
10.22075/ijnaa.2016.481
481
A generalization of Martindale's theorem to $(alpha, beta)-$homomorphism
Eqbal Keyhani
kayhanymath@gmail.com
1
Mahmoud Hassani
mhassanimath@gmail.com
2
Maryam Amyari
amyari@mshdiau.ac.ir
3
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
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.
https://ijnaa.semnan.ac.ir/article_481_ad67ee626a0c5ed5b5884900645f4b81.pdf
beta)-$multiplicative mapping
beta)-$multiplicative isomorphism
$(alpha
beta)-$additive mapping
multiplicative $(alpha
beta)-$derivations
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-11-17
7
2
153
164
10.22075/ijnaa.2016.456
456
Algebras defined by homomorphisms
Feysal Hassani
feysal.hassani.pnu@gmail.com
1
Payame Noor University
Let $mathcal{R}$ be a commutative ring with identity, let $A$ and $B$ be two $mathcal{R}$-algebras and $varphi:Blongrightarrow A$ be an $mathcal{R}$-additive algebra homomorphism. We introduce a new algebra $Atimes_varphi B$, and give some basic properties of this algebra. Generalized $2$-cocycle derivations on $Atimes_varphi B$ are studied. Accordingly, $Atimes_varphi B$ is considered from the perspective of Banach algebras.
https://ijnaa.semnan.ac.ir/article_456_802d5ab4109a34749b6a7c2c7798aea9.pdf
algebra
cocycle
generalized derivation
Banach algebra
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-26
7
2
165
184
10.22075/ijnaa.2017.520
520
On boundary value problems of higher order abstract fractional integro-differential equations
Sabri T. M. Thabet
th.sabri@yahoo.com
1
Machindra B. Dhakne
mbdhakne@yahoo.com
2
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University,
Aurangabad - 431004, Maharashtra, India.
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad - 431004, Maharashtra, India.
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.
https://ijnaa.semnan.ac.ir/article_520_194aeb0c75105fe3eb3c003fb975b20e.pdf
Fractional integro-differential equations
boundary value problem
fixed point theorems
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-15
7
2
185
193
10.22075/ijnaa.2017.1080.1228
2262
Existence of Mild Solutions to a Cauchy Problem Presented by Fractional Evolution Equation with an Integral Initial Condition
Mohamad Hossein Akrami
akrami@yazd.ac.ir
1
Gholam Hussain Erjaee
erjaee@shirazu.ac.ir
2
Department of Mathematics, Yazd University, Yazd, Iran.
Department of Mathematics, College of Science, Shiraz University, 74811-71466 Shiraz, Iran
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.
https://ijnaa.semnan.ac.ir/article_2262_c2b9bd3c99a66a2db8f761f296a64c4b.pdf
Fractional evolution equation
Cauchy problem
Fixed point theorem
Mild solution
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-25
7
2
195
204
10.22075/ijnaa.2017.1332.1329
2263
Approximation of a generalized Euler-Lagrange type additive mapping on Lie $C^{ast}$-algebras
Zhihua Wang
20061062@hbut.edu.cn
1
Prasanna K. Sahoo
sahoo@louisville.edu
2
School of Science, Hubei University of Technology, Wuhan, Hubei 430068, P.R. China
Department of Mathematics, University of Louisville, Louisville, KY 40292, USA
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_{1leq i leq n, ineq<br /> j}r_{i}x_{i}bigg)}+2sum^{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 $1leq i< jleq n$.
https://ijnaa.semnan.ac.ir/article_2263_c8c5159b5ec222ee67da73e89bf61592.pdf
Fixed point theorem
Lie $(alpha,beta,gamma)$-derivation
Lie $C^{ast}$-algebra homomorphisms
generalized Hyers-Ulam stability
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-18
7
2
205
216
10.22075/ijnaa.2017.1074.1222
2264
Existence of solutions of infinite systems of integral equations in the Frechet spaces
Reza Arab
mathreza.arab@iausari.ac.ir
1
Reza Allahyari
rezaallahyari@mshdiau.ac.ir
2
Ali Shole Haghighi
ali.sholehaghighi@gmail.com
3
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.
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.
https://ijnaa.semnan.ac.ir/article_2264_d473862b05d2a18a6a30b75788356ff0.pdf
Measure of noncompactness
Frechet space
Tychonoff fixed point theorem
Infinite systems of equations
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-11-15
7
2
217
228
10.22075/ijnaa.2017.10452.1504
2272
Some common fixed point theorems for Gregus type mappings
Sumit Chandok
chansok.s@gmail.com
1
School of Mathematics, Thapar University, Patiala-147004, Punjab, India
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.
https://ijnaa.semnan.ac.ir/article_2272_ae88375151c0dfb6fc680b0a1f00781f.pdf
Common fixed point
convex set
commuting maps
compatible maps
compatible maps of type (A)
compatible maps of type (B)
affine map
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-10-14
7
2
229
242
10.22075/ijnaa.2017.10573.1510
2308
A contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies
John Venetis
johnvenetis4@gmail.com
1
Emilios Sideridis
siderem@mail.ntua.gr
2
School of Applied Mathematics and Physical Sciences NTUA, Section of Mechanics, 5 Heroes of Polytechnion Avenue GR,15773 Athens, Greece
School of Applied Mathematics and Physical Sciences NTUA, Section of Mechanics, 5 Heroes of Polytechnion Avenue GR,15773 Athens, Greece.
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.
https://ijnaa.semnan.ac.ir/article_2308_89fe59563da22b632b56d4c4ff3a0620.pdf
Orthogonal functions
Abel's summability
Poisson's kernel
Von Karman's spectrum
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-11-16
7
2
243
251
10.22075/ijnaa.2016.501
501
Projected non-stationary simultaneous iterative methods
Touraj Nikazad
tnikazad@iust.ac.ir
1
Mahdi Mirzapour
mahdimirzapour67@gmail.com
2
School of Mathematics,
Iran University of Science and Technology
School of Mathematics, Iran University of Science and Technology
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.
https://ijnaa.semnan.ac.ir/article_501_d9a27af16a0f373c8ccda25b95136ec7.pdf
Simultaneous iterative reconstruction techniques
convex feasibility problem
(firmly) nonexpansive operator
cutter operator
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-02
7
2
253
267
10.22075/ijnaa.2017.980.1185
2309
Random fractional functional differential equations
Vu Ho
hovumath@gmail.com
1
Institute for Computational Science
Ton Duc Thang University;
19 Nguyen Huu Tho, District 7, Ho Chi Minh City, Vietnam
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.
https://ijnaa.semnan.ac.ir/article_2309_3b8da04d29148ca35bf85766e16ab224.pdf
Sample fractional integral
Sample fractional derivative
Fractional differential equations
random differential equations
Caputo fractional derivative
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-11-08
7
2
269
277
10.22075/ijnaa.2016.458
458
Differential transform method for a a nonlinear system of differential equations arising in HIV infection of CD4+T cell
Javad Damirchi
damirchi.javad@gmail.com
1
Taher Rahimi shamami
rahimishamami2012@gmail.com
2
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University,Semnan, Iran
Department of Mathematics, Faculsty of Mathematics, Statistics and Computer Science, Semnan University, Semnan Iran
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.
https://ijnaa.semnan.ac.ir/article_458_eb4989c1d76da877a5c06a66b8d994fd.pdf
Differential transform method
Systems of nonlinear ordinary differential equations
Pade approximation
Fourth order Runge-Kutta method
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-09
7
2
279
301
10.22075/ijnaa.2017.1803.1472
774
Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations
Th.M. Rassias
trassias@math.ntua.gr
1
Elhoucien Elqorachi
elqorachi@hotmail.com
2
Ahmed Redouani
redouani−ahmed@yahoo.fr
3
Department of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, Greece
Ibn Zohr University, Faculty of Sciences Department of Mathematic, Agadir, Morocco
Ibn Zohr University, Faculty of Sciences Department of Mathematic, Agadir, Morocco
In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation<br /> $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ 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 $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{i}$ 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 /> $$int_{S}f(xty)dupsilon(t)+int_{S}f(sigma(y)tx)dupsilon(t) = 2f(x)f(y), ;x,yin S,$$ 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.
https://ijnaa.semnan.ac.ir/article_774_ac5ba88e6d8ed3f180cc2ff75a074111.pdf
semigroup
d'Alembert's equation
Van Vleck's equation, sine function
involution
multiplicative function, homomorphism, superstability
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-19
7
2
303
318
10.22075/ijnaa.2016.505
505
Fractional dynamical systems: A fresh view on the local qualitative theorems
Khosro Sayevand
ksayehvand@malayeru.ac.ir
1
Faculty of Mathematical Sciences, Malayer University, P.O.Box 16846-13114, Malayer, Iran
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.
https://ijnaa.semnan.ac.ir/article_505_6dd6f750a1f5b7ac40e8c8f4e08ab830.pdf
Fractional differential systems
Stable manifold theorem
Hartman-Grobman theorem
Local center manifold theorem
Local qualitative theory
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-30
7
2
319
329
10.22075/ijnaa.2017.1301.1320
2317
Asymptotic behavior of a system of two difference equations of exponential form
Mai Nam Phong
mnphong@utc.edu.vn
1
Vu Van Khuong
vuvankhuong@gmail.com
2
Department of Mathematical Analysis, University of Transport and Communications, Hanoi City, Vietnam
Department of Mathematical Analysis, University of Transport and Communications, Hanoi City, Vietnam
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.
https://ijnaa.semnan.ac.ir/article_2317_fd9ef87284cd65c4c0051d2f2524b18c.pdf
Difference equations
boundedness
persistence
asymptotic behavior
rate of convergence
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-01
7
2
331
343
10.22075/ijnaa.2017.1129.1249
2319
A numerical scheme for space-time fractional advection-dispersion equation
Shahnam Javadi
javadi@khu.ac.ir
1
Mostafa Jani
std_jani@khu.ac.ir
2
Esmail Babolian
babolian@khu.ac.ir
3
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
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.
https://ijnaa.semnan.ac.ir/article_2319_26e1ee558045f8ddff548d3f3b47e268.pdf
Advection-dispersion equation
Space-time fractional PDE
Bernstein polynomials
Product integration
Spectral-collocation
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-11-08
7
2
345
349
10.22075/ijnaa.2016.2320
2320
On some generalisations of Brown's conjecture
Bashir Ahmad Zargar
bazargar@gmail.com
1
Manzoor Ahmad
mwali@gmail.com
2
Department of Mathematics, University of Kashmir, Hazratbal, Srinagar
Department of Mathematics, University of Kashmir, Hazratbal, Srinagar
Let $P$ be a complex polynomial of the form $P(z)=zdisplaystyleprod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|ge 1,1le kle n-1$ then $ P^prime(z)ne 0$. If $|z|<dfrac {1}{n}$. In this paper, we present some interesting generalisations of this result.
https://ijnaa.semnan.ac.ir/article_2320_2cb9da095415c881426e1ad3495e119c.pdf
Critical points
Sendove's Conjecture
Coincidence theorem of walsh
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-26
7
2
351
362
10.22075/ijnaa.2017.1241.1296
2321
Existence of three solutions for a class of fractional boundary value systems
Samad Mohseni Kolagar
mohseni.samad@gmail.com
1
Ghasem A. Afrouzi
afrouzi@umz.ac.ir
2
Armin Hadjian
hadjian83@gmail.com
3
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran
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.
https://ijnaa.semnan.ac.ir/article_2321_5863ebd05baaf26bc703c4dde8cca5ba.pdf
Fractional differential equations
Riemann-Liouville fractional derivatives
Variational methods
Three solutions
eng
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
2008-6822
2016-12-30
7
2
363
374
10.22075/ijnaa.2017.2322
2322
On best proximity points for multivalued cyclic $F$-contraction mappings
Konrawut Khammahawong
k.konrawut@gmail.com
1
Parinya Sa Ngiamsunthorn
parinya.san@kmutt.ac.th
2
Poom Kumam
poom.kum@kmtt.ac.th
3
King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
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.
King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
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.
https://ijnaa.semnan.ac.ir/article_2322_a14950d6213380e677cbc576639e0d60.pdf
best proximity point
cyclic contraction
$F$-contraction
multivalued mapping
metric space