2021-11-27T05:29:48Z
https://ijnaa.semnan.ac.ir/?_action=export&rf=summon&issue=71
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
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
Bicheng
Yang
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
2016
06
01
1
27
https://ijnaa.semnan.ac.ir/article_375_c8b2e9a805289b56d307b04d2e8cc8c1.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition
Somayeh
Saiedinezhad
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.
Hardy type inequality
Variable exponent Lebesgue space
Modular type inequality.
2016
07
01
29
38
https://ijnaa.semnan.ac.ir/article_439_a9ff1b7775e024c726cd0418c812bd7b.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Weak and $(-1)$-weak amenability of second dual of Banach algebras
A.
Valadkhani
S.A.R.
Hosseinioun
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
2016
06
01
39
48
https://ijnaa.semnan.ac.ir/article_457_caf6063aacac36ba84aaec150ac133f2.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Fixed points for Chatterjea contractions on a metric space with a graph
Kamal
Fallahi
Aris
Aghanians
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
2016
05
05
49
58
https://ijnaa.semnan.ac.ir/article_449_28e573679a0823fddb453f5c119bc3ee.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Application of new basis functions for solving nonlinear stochastic differential equations
Zahra
Sadati
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
2016
09
09
59
68
https://ijnaa.semnan.ac.ir/article_450_5a634288d0d55d50b7448802c0a9f43d.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
( p,q)-Genuine Baskakov-Durrmeyer operators
Vijay
Gupta
Th.
Rassias
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
2016
07
01
69
76
https://ijnaa.semnan.ac.ir/article_454_0436ce511d55e45b51b5f1bf2fc99a3d.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Coincidence point and common fixed point results via scalarization function
Sushanta
Mohanta
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
2016
06
12
77
91
https://ijnaa.semnan.ac.ir/article_478_fcdfd8b1214eedc472509c9cb0d177f6.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings
Godwin
Ugwunnadi
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
2016
08
06
93
108
https://ijnaa.semnan.ac.ir/article_479_faac311c75f79ded9e0cb8b61b577217.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Product of derivations on C$^*$-algebras
Khalil
Ekrami
Madjid
Mirzavaziri
Hamid Reza
Ebrahimi Vishki
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
2016
12
30
109
114
https://ijnaa.semnan.ac.ir/article_451_0bbbe5991acf696ef672151434ad1e2a.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Some drifts on posets and its application to fuzzy subalgebras
Xiaohong
Zhang
Hee Sik
Kim
Joseph
Neggers
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
2016
12
01
115
125
https://ijnaa.semnan.ac.ir/article_503_0e526cbeda0c0cac76e960d4f005b888.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
The solutions to the operator equation $TXS^* -SX^*T^*=A$ in Hilbert $C^*$-modules
Mehdi
Mohammadzadeh Karizaki
Mahmoud
Hassani
Dragan
Djordjevic
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
2016
11
14
127
132
https://ijnaa.semnan.ac.ir/article_502_53db64a878b47ab121fa3552645e4306.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Some inequalities in connection to relative orders of entire functions of several complex variables
Sanjib
Datta
Tanmay
Biswas
Debasmita
Dutta
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
2016
12
03
133
141
https://ijnaa.semnan.ac.ir/article_518_df28fc621a27f6e4fc6e1ec5be008124.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
A generalization of Martindale's theorem to $(alpha, beta)-$homomorphism
Eqbal
Keyhani
Mahmoud
Hassani
Maryam
Amyari
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
2016
06
01
143
151
https://ijnaa.semnan.ac.ir/article_481_ad67ee626a0c5ed5b5884900645f4b81.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Algebras defined by homomorphisms
Feysal
Hassani
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
2016
11
17
153
164
https://ijnaa.semnan.ac.ir/article_456_802d5ab4109a34749b6a7c2c7798aea9.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
On boundary value problems of higher order abstract fractional integro-differential equations
Sabri T. M.
Thabet
Machindra B.
Dhakne
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
2016
12
26
165
184
https://ijnaa.semnan.ac.ir/article_520_194aeb0c75105fe3eb3c003fb975b20e.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Existence of Mild Solutions to a Cauchy Problem Presented by Fractional Evolution Equation with an Integral Initial Condition
Mohamad Hossein
Akrami
Gholam Hussain
Erjaee
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
2016
12
15
185
193
https://ijnaa.semnan.ac.ir/article_2262_c2b9bd3c99a66a2db8f761f296a64c4b.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Approximation of a generalized Euler-Lagrange type additive mapping on Lie $C^{ast}$-algebras
Zhihua
Wang
Prasanna K.
Sahoo
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 $1\leq i< j\leq n$.
Fixed point theorem
Lie $(alpha,beta,gamma)$-derivation
Lie $C^{ast}$-algebra homomorphisms
generalized Hyers-Ulam stability
2016
12
25
195
204
https://ijnaa.semnan.ac.ir/article_2263_c8c5159b5ec222ee67da73e89bf61592.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Existence of solutions of infinite systems of integral equations in the Frechet spaces
Reza
Arab
Reza
Allahyari
Ali
Shole Haghighi
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
2016
12
18
205
216
https://ijnaa.semnan.ac.ir/article_2264_d473862b05d2a18a6a30b75788356ff0.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Some common fixed point theorems for Gregus type mappings
Sumit
Chandok
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.
Common fixed point
convex set
commuting maps
compatible maps
compatible maps of type (A)
compatible maps of type (B)
affine map
2016
11
15
217
228
https://ijnaa.semnan.ac.ir/article_2272_ae88375151c0dfb6fc680b0a1f00781f.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
A contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies
John
Venetis
Emilios
Sideridis
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
2016
10
14
229
242
https://ijnaa.semnan.ac.ir/article_2308_89fe59563da22b632b56d4c4ff3a0620.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Projected non-stationary simultaneous iterative methods
Touraj
Nikazad
Mahdi
Mirzapour
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
2016
11
16
243
251
https://ijnaa.semnan.ac.ir/article_501_d9a27af16a0f373c8ccda25b95136ec7.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Random fractional functional differential equations
Vu
Ho
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
2016
12
02
253
267
https://ijnaa.semnan.ac.ir/article_2309_3b8da04d29148ca35bf85766e16ab224.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Differential transform method for a a nonlinear system of differential equations arising in HIV infection of CD4+T cell
Javad
Damirchi
Taher
Rahimi shamami
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
2016
11
08
269
277
https://ijnaa.semnan.ac.ir/article_458_eb4989c1d76da877a5c06a66b8d994fd.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations
Th.M.
Rassias
Elhoucien
Elqorachi
Ahmed
Redouani
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.
semigroup
d'Alembert's equation
Van Vleck's equation, sine function
involution
multiplicative function, homomorphism, superstability
2016
12
09
279
301
https://ijnaa.semnan.ac.ir/article_774_ac5ba88e6d8ed3f180cc2ff75a074111.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Fractional dynamical systems: A fresh view on the local qualitative theorems
Khosro
Sayevand
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
2016
12
19
303
318
https://ijnaa.semnan.ac.ir/article_505_6dd6f750a1f5b7ac40e8c8f4e08ab830.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Asymptotic behavior of a system of two difference equations of exponential form
Mai Nam
Phong
Vu Van
Khuong
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.
Difference equations
boundedness
persistence
asymptotic behavior
rate of convergence
2016
12
30
319
329
https://ijnaa.semnan.ac.ir/article_2317_fd9ef87284cd65c4c0051d2f2524b18c.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
A numerical scheme for space-time fractional advection-dispersion equation
Shahnam
Javadi
Mostafa
Jani
Esmail
Babolian
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
2016
12
01
331
343
https://ijnaa.semnan.ac.ir/article_2319_26e1ee558045f8ddff548d3f3b47e268.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
On some generalisations of Brown's conjecture
Bashir Ahmad
Zargar
Manzoor
Ahmad
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
2016
11
08
345
349
https://ijnaa.semnan.ac.ir/article_2320_2cb9da095415c881426e1ad3495e119c.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
Existence of three solutions for a class of fractional boundary value systems
Samad
Mohseni Kolagar
Ghasem A.
Afrouzi
Armin
Hadjian
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
2016
12
26
351
362
https://ijnaa.semnan.ac.ir/article_2321_5863ebd05baaf26bc703c4dde8cca5ba.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2016
7
2
On best proximity points for multivalued cyclic $F$-contraction mappings
Konrawut
Khammahawong
Parinya
Sa Ngiamsunthorn
Poom
Kumam
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
2016
12
30
363
374
https://ijnaa.semnan.ac.ir/article_2322_a14950d6213380e677cbc576639e0d60.pdf