Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220160601A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function12737510.22075/ijnaa.2016.375ENMichael Th. RassiasInstitute of Mathematics, University of Zurich, CH-8057, Zurich, Switzerland \\ \& Institute for Advanced Study, Program in Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ 08540, USABicheng YangDepartment of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. ChinaJournal Article20150511By 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220160701Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition293843910.22075/ijnaa.2016.439ENSomayeh SaiedinezhadAssistant professor of Iran University of Science and technologyJournal Article20151205Some 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220160601Weak and $(-1)$-weak amenability of second dual of Banach algebras394845710.22075/ijnaa.2016.457ENA. ValadkhaniUniversity of Simon Fraser, Department of Education, Vancouver, CanadaS.A.R. HosseiniounUniversity of Arkansas, Department of Mathematical sciences, Fayetteville, AR 72703, USAJournal Article20151219For 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220160505Fixed points for Chatterjea contractions on a metric space with a graph495844910.22075/ijnaa.2016.449ENKamal FallahiDepartment of Mathematics, Payame Noor University,
P.O. Box 19395-3697, Tehran, IranAris AghaniansDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, IranJournal Article20141223In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220160909Application of new basis functions for solving nonlinear stochastic differential equations596845010.22075/ijnaa.2016.450ENZahra SadatiDepartment of Mathematics, khomein Branch, Islamic Azad University, khomein, IranJournal Article20140519This 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220160701( p,q)-Genuine Baskakov-Durrmeyer operators697645410.22075/ijnaa.2016.454ENVijay GuptaNetaji Subhas Institute of Technology
New Delhi, IndiaTh. M.RassiasNational Technical University of Athens
Department of Mathematics
Zografou Campus,
GR-15780, Athens, GreeceJournal Article20151218In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220160612Coincidence point and common fixed point results via scalarization function779147810.22075/ijnaa.2016.478ENSushanta MohantaWest Bengal State University, Barasat, 24 Parganas(North), Kolkata-700126, West Bengal, IndiaJournal Article20140809The 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220160806Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings9310847910.22075/ijnaa.2016.479ENGodwin ChidiUgwunnadiMichael Okpara University of Agriculture, Umudike, Abia State, NigeriaJournal Article20140824In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161230Product of derivations on C$^*$-algebras10911445110.22075/ijnaa.2017.451ENKhalil EkramiDepartment of Mathematics, Payame Noor UniversityMadjid MirzavaziriDepartment of Pure Mathematics and Center of Excellence in Analysis on Algebraic Struc-tures (CEAAS), Ferdowsi University of MashhadHamid Reza Ebrahimi VishkiDepartment of Pure Mathematics and Center of Excellence in Analysis on Algebraic Struc-tures (CEAAS), Ferdowsi University of Mashhad,Journal Article20160717Let $mathfrak{A}$ 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 $sinmathbb{C}$.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161201Some drifts on posets and its application to fuzzy subalgebras11512550310.22075/ijnaa.2016.503ENXiaohong ZhangCollege of Arts and Sciences
Shanghai Maritime UniversityHee Sik KimResearch Institute for Natural Sci., Department of Mathematics, Hanyang University, Seoul, 04763, KoreaJoseph NeggersDepartment of Mathematics
University of AlabamaJournal Article20151218In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161114The solutions to the operator equation $TXS^* -SX^*T^*=A$ in Hilbert $C^*$-modules12713250210.22075/ijnaa.2016.502ENMehdi Mohammadzadeh KarizakiDepartment of Mathematics,
Mashhad Branch, Islamic Azad University,
Mashhad 91735, IranMahmoud HassaniDepartment of Mathematics, Mashhad Branch, Islamic Azad University,
Mashhad, Iran.Dragan DjordjevicD. S. Djordjevic, Faculty of Sciences and Mathematics, University of ´
Nis, Visegradska 33, P.O. Box 224, 18000 Nis, Serbia.Journal Article20151119In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161203Some inequalities in connection to relative orders of entire functions of several complex variables13314151810.22075/ijnaa.2016.518ENSanjib KumarDattaAssociate Professor
Department of Mathematics
University of KalyaniTanmay BiswasRajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar, Dist-Nadia,PIN-741101, West Bengal, IndiaDebasmita DuttaMohanpara Nibedita Balika Vidyalaya (High),P.o - Amrity, Block - English Bazar, Dist.- District - Malda, PIN- 732208, West Bengal, IndiaJournal Article20150712Let 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220160601A generalization of Martindale's theorem to $(alpha, beta)-$homomorphism14315148110.22075/ijnaa.2016.481ENEqbal KeyhaniDepartment of Mathematics, Mashhad Branch, Islamic Azad University,
Mashhad, Iran.Mahmoud HassaniDepartment of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, IranMaryam AmyariDepartment of Mathematics, Mashhad Branch, Islamic Azad University,
Mashhad, Iran.Journal Article20150116Martindale 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161117Algebras defined by homomorphisms15316445610.22075/ijnaa.2016.456ENFeysal HassaniPayame Noor UniversityJournal Article20160915Let $mathcal{R}$ 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161226On boundary value problems of higher order abstract fractional integro-differential equations16518452010.22075/ijnaa.2017.520ENSabri T. M. ThabetDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University,
Aurangabad - 431004, Maharashtra, India.Machindra B. DhakneDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad - 431004, Maharashtra, India.Journal Article20150825The 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161215Existence of Mild Solutions to a Cauchy Problem Presented by Fractional Evolution Equation with an Integral Initial Condition185193226210.22075/ijnaa.2017.1080.1228ENMohamad Hossein AkramiDepartment of Mathematics, Yazd University, Yazd, Iran.Gholam Hussain ErjaeeDepartment of Mathematics, College of Science, Shiraz University, 74811-71466 Shiraz, IranJournal Article20151221In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161225Approximation of a generalized Euler-Lagrange type additive mapping on Lie $C^{ast}$-algebras195204226310.22075/ijnaa.2017.1332.1329ENZhihua WangSchool of Science, Hubei University of Technology, Wuhan, Hubei 430068, P.R. ChinaPrasanna K. SahooDepartment of Mathematics, University of Louisville, Louisville, KY 40292, USAJournal Article20160417Using 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 $1leq i< jleq n$.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161218Existence of solutions of infinite systems of integral equations in the Frechet spaces205216226410.22075/ijnaa.2017.1074.1222ENReza ArabDepartment of Mathematics, Sari Branch, Islamic Azad University, Sari, IranReza AllahyariDepartment of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.Ali Shole HaghighiDepartment of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.Journal Article20151219In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161115Some common fixed point theorems for Gregus type mappings217228227210.22075/ijnaa.2017.10452.1504ENSumit ChandokSchool of Mathematics, Thapar University, Patiala-147004, Punjab, IndiaJournal Article20140803In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161014A contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies229242230810.22075/ijnaa.2017.10573.1510ENJohn VenetisSchool of Applied Mathematics and Physical Sciences NTUA, Section of Mechanics, 5 Heroes of Polytechnion Avenue GR,15773 Athens, GreeceEmilios SideridisSchool of Applied Mathematics and Physical Sciences NTUA, Section of Mechanics, 5 Heroes of Polytechnion Avenue GR,15773 Athens, Greece.Journal Article20140212In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161116Projected non-stationary simultaneous iterative methods24325150110.22075/ijnaa.2016.501ENTouraj NikazadSchool of Mathematics,
Iran University of Science and TechnologyMahdi MirzapourSchool of Mathematics,
Iran University of Science and TechnologyJournal Article20151008In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161202Random fractional functional differential equations253267230910.22075/ijnaa.2017.980.1185ENVu HoInstitute for Computational Science
Ton Duc Thang University;
19 Nguyen Huu Tho, District 7, Ho Chi Minh City, VietnamJournal Article20151028In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161108Differential transform method for a a nonlinear system of differential equations arising in HIV infection of CD4+T cell26927745810.22075/ijnaa.2016.458ENJavad DamirchiDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University,Semnan, IranTaher Rahimi shamamiDepartment of Mathematics, Faculsty of Mathematics, Statistics and Computer Science, Semnan University, Semnan IranJournal Article20160102In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161209Solutions and stability of variant of Van Vleck's and D'Alembert's functional equations27930177410.22075/ijnaa.2017.1803.1472ENTh.M. RassiasDepartment of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, GreeceElhoucien ElqorachiIbn Zohr University, Faculty of Sciences
Department of Mathematic, Agadir, MoroccoAhmed RedouaniIbn Zohr University, Faculty of Sciences
Department of Mathematic, Agadir, MoroccoJournal Article20151220In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161219Fractional dynamical systems: A fresh view on the local qualitative theorems30331850510.22075/ijnaa.2016.505ENKhosro SayevandFaculty of Mathematical Sciences, Malayer University, P.O.Box 16846-13114, Malayer, IranJournal Article20160205The 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161230Asymptotic behavior of a system of two difference equations of exponential form319329231710.22075/ijnaa.2017.1301.1320ENMai Nam PhongDepartment of Mathematical Analysis, University of Transport and Communications, Hanoi City, VietnamVu Van KhuongDepartment of Mathematical Analysis, University of Transport and Communications, Hanoi City, VietnamJournal Article20160331In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161201A numerical scheme for space-time fractional advection-dispersion equation331343231910.22075/ijnaa.2017.1129.1249ENShahnam JavadiDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi UniversityMostafa JaniDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, IranEsmail BabolianDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, IranJournal Article20160112In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161108On some generalisations of Brown's conjecture345349232010.22075/ijnaa.2016.2320ENBashir Ahmad ZargarDepartment of Mathematics, University of Kashmir, Hazratbal, SrinagarManzoor AhmadDepartment of Mathematics, University of Kashmir, Hazratbal, SrinagarJournal Article20150226Let $P$ 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161226Existence of three solutions for a class of fractional boundary value systems351362232110.22075/ijnaa.2017.1241.1296ENSamad Mohseni KolagarDepartment of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, IranGhasem A. AfrouziDepartment of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, IranArmin HadjianDepartment of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, IranJournal Article20160301In 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.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227220161230On best proximity points for multivalued cyclic $F$-contraction mappings363374232210.22075/ijnaa.2017.2322ENKonrawut KhammahawongKing Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandParinya Sa NgiamsunthornDepartment of Mathematics,
Faculty of Science,
King Mongkut’s University of Technology Thonburi (KMUTT),
126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand.Poom KumamKing Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandJournal Article20160605In 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.