Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160211Relative order and type of entire functions represented by Banach valued Dirichlet series in two variables11428810.22075/ijnaa.2016.288ENDibyenduBanerjeeDepartment of Mathematics, Visva-Bharati, Santiniketan- 731235, IndiaNilkantaMondalBallavpur R.G.S.Vidyapith, Ballavpur-713323, Raniganj, IndiaJournal Article20141111In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results. Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of its partial derivative.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120151211On the quadratic support of strongly convex functions152027310.22075/ijnaa.2015.273ENS.AbbaszadehDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, IranMEshaghi GordjiDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, IranJournal Article20131211In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120151210Nonexpansive mappings on complex C*-algebras and their fixed points212928910.22075/ijnaa.2015.289ENDavoodAlimohammadiDepartment of Mathematics, Faculty of Science, Arak university, Arak 38156-8-8349, Iran0000-0002-9398-6213Journal Article20150607A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (iii) $C_0 (X)$ does not have the fixed point property. We also show that if $A$ is a commutative complex $mathsf{C}^*$-algebra with nonempty carrier space, then the following statements are equivalent: (i) Carrier space of $ A $ is infinite, (ii) $ A $ is infinite dimensional, (iii) $ A $ does not have the fixed point property. Moreover, we show that if $ A $ is an infinite complex $mathsf{C}^*$-algebra (not necessarily commutative), then $ A $ does not have the fixed point property.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160121On the fine spectrum of generalized upper triangular double-band matrices $Delta^{uv}$ over the sequence spaces $c_o$ and $c$314329010.22075/ijnaa.2015.290ENJavadFathiDepartment of Mathematic, Faculty of Science, Hormozgan University, Bandarabbas, IranJournal Article20131108The main purpose of this paper is to determine the fine spectrum of the generalized upper triangular double-band matrices $Delta^{uv}$ over the sequence spaces $c_o$ and $c$. These results are more general than the spectrum of upper triangular double-band matrices of Karakaya and Altun [V. Karakaya, M. Altun, Fine spectra of upper triangular doubleband matrices, Journal of Computational and Applied Mathematics, 234(2010) 1387-1394].Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160127Common fixed point theorem for nonexpansive type single valued mappings455129310.22075/ijnaa.2015.293ENPankaj KumarJhadeNRI Institute of Information Science & Technology, Bhopal, MP, 462021, IndiaA. S.SalujaJ H Govt. PG College, Betul, 460001, IndiaJournal Article20131013The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of nonexpansive type multivalued and single valued maps, European J. Pure Appl. Math., 4 (2011) 330-339].Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160201Some fixed point theorems for weakly subsequentially continuous and compatible of type (E) mappings with an application536229410.22075/ijnaa.2015.294ENSaidBeloulDepartment of Mathematics and Informatics, Faculty of Sciences and Technology, University of Eloued, P.O.Box 789,
Eloued 39000, AlgeriaJournal Article20141010In this paper, we will establish some fixed point results for two pairs of self mappings satisfying generalized contractive condition by using a new concept as weak subsequential continuity with compatibility of type (E) in metric spaces, as an application the existence of unique common solution for a system of functional equations arising in system programming is proved.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160204Approximate a quadratic mapping in multi-Banach spaces, a fixed point approach637529510.22075/ijnaa.2015.295ENSattarAlizadehDepartment of Mathematics, Marand Branch, Islamic Azad University, Marand, IranFridounMoradlouDepartment of Mathematics, Sahand University of Technology, Tabriz, IranJournal Article20141010Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:<br />begin{equation}<br />sum_{ j = 1}^{n}fBig(-2 x_{j} + sum_{ i = 1, neq j}^{n} x_{i}Big) =<br />(n-6) fBig(sum_{ i = 1}^{n} x_{i}Big) + 9 sum_{ i = 1}^{n}<br />f(x_{i}).<br />end{equation}Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160218On the generalization of Trapezoid Inequality for functions of two variables with bounded variation and applications778529610.22075/ijnaa.2015.296ENHuseyinBudakDepartment of Mathematics, Faculty of Science and Arts, Duzce University, Duzce, Turkey0000-0001-8843-955XMehmetSarikayaDepartment of Mathematics, Faculty of Science and Arts, Duzce University, Duzce, TurkeyJournal Article20141121In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160227Generalized solution of Sine-Gordon equation879229710.22075/ijnaa.2015.297ENLalla SaadiaChadliLaboratoire de Mathematiques Appliquees & Calcul Ssientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni
Mellal, MoroccoSaidMellianiLaboratoire de Mathematiques Appliquees & Calcul Ssientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni
Mellal, MoroccoAbdelazizMoujahidLaboratoire de Mathematiques Appliquees & Calcul Ssientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni
Mellal, MoroccoMhamedElomariLaboratoire de Mathematiques Appliquees & Calcul Ssientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni
Mellal, MoroccoJournal Article20140317In this paper, we are interested to study the Sine-Gordon equation in generalized functions theory introduced by Colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the Colombeau algebra). Then we study the association concept with the classical solution.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160301Titchmarsh theorem for Jacobi Dini-Lipshitz functions9310129810.22075/ijnaa.2015.298ENMustaphaBoujeddaineDepartment of Mathematics and Computer Sciences, Faculty of Sciences, Equipe d Analyse Harmonique et Probabilies, Universite Moulay Ismail,
BP 11201 Zitoune, Meknes, MoroccoSaidFahlaouiDepartment of Mathematics and Computer Sciences, Faculty of Sciences, Equipe d Analyse Harmonique et Probabilies, Universite Moulay Ismail,
BP 11201 Zitoune, Meknes, MoroccoRadouanDaherDepartment of Mathematics, Faculty of Sciences An Chock,
University of Hassan II, BP 5366, Maarif, Casablanca, MoroccoJournal Article20141002Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lipschitz condition in $L^{p}$.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120151216Some new results using Hadamard fractional integral10310929910.22075/ijnaa.2015.299ENSabrinaTafDepartment of Mathematic, Faculty SEI, UMAB University of Mostaganem, AlgeriaKamelBrahimFaculty of science of Tunis, TunisiaJournal Article20140412Fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order. The purpose of this work is to use Hadamard fractional integral to establish some new integral inequalities of Gruss type by using one or two parameters which ensues four main results . Furthermore, other integral inequalities of reverse Minkowski's type are obtained for positive functions resulting in two theorems.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120151117Some common fixed point theorems for four $(psi,varphi)$-weakly contractive mappings satisfying rational expressions in ordered partial metric spaces11113030010.22075/ijnaa.2015.300ENR.A.RashwanDepartment of Mathematics, Faculty of Science, Assiut University, Assiut, EgyptS.M.SalehDepartment of Mathematics, Faculty of Science, Assiut University, Assiut, EgyptJournal Article20130709The aim of this paper is to prove some common fixed point theorems for four mappings satisfying $(psi,varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give two examples to illustrate our results.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160107A determinant inequality and log-majorisation for operators13114030110.22075/ijnaa.2015.301ENSeyed MahmoudManjeganiDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 84156-83111Journal Article20150310Let $lambda_1,dots,lambda_n$ be positive real numbers such that $sum_{k=1}^n lambda_k=1$. In this paper, we prove that for any positive operators $a_1,a_2,ldots, a_n$ in semifinite von Neumann algebra $M$ with faithful normal trace that $t(1)<infty$, $$prod_{k=1}^n(det a_k)^{lambda_k},le,det (sum_{k=1}^n lambda_k a_k),$$<br />where $det a=exp(int_0^{t(1)} mu_a(t),dt)$. If furthermore $t(a_i)<infty$ for every $1le ile n$ and $ prod_{k=1}^n(det a_k)^{lambda_k}neq 0$,<br /> then equality holds if and only if $a_1=a_2=cdots =a_n$. A log-majorisation version of Young inequality are given as well.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120151101On the $s^{th}$ derivative of a polynomial14114513010.22075/ijnaa.2015.130ENAbdullahMirDepartment of Mathematics, University of Kashmir, Srinagar, $190006$, (India)Journal Article20131024For every $1leq s< n$, the $s^{th}$ derivative of a polynomial $P(z)$ of degree $n$ is a polynomial $P^{(s)}(z)$ whose degree is $(n-s)$. This paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. Besides, our result gives interesting refinements of some well-known results.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160115Vector ultrametric spaces and a fixed point theorem for correspondences14715330210.22075/ijnaa.2015.302ENKouroshNourouziFaculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, IranJournal Article20141130In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120151130Variational inequalities on Hilbert $C^*$-modules15516530310.22075/ijnaa.2015.303ENHedayatFathiDepartment of Mathematics, Shahid Beheshti University, Tehran, IranS.A.R.HosseiniounDepartment of Mathematics, Shahid Beheshti University, Tehran, Iran;
Department of Mathematics, University of Arkansas,
Fayetteville, Arkansas 72701, USAJournal Article20141208We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory on Hilbert $C^*$-modules is studied.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160319Approximately generalized additive functions in several variables via fixed point method16718130410.22075/ijnaa.2015.304ENR.Farokhzad RostamiDepartment of Mathematics, Gonbad Kavous University, Gonbad Kavous, Golestan, Iran0000-0002-3965-2634S.A.R.HoseiniounDepartment of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USAJournal Article20141014In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability in random normed spaces, in non-Archimedean spaces and also in $p$-Banach spaces and finally the stability via fixed point method for a functional equation<br />begin{align*}<br />&D_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}<br />sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1})<br /> f(sum^{m}_{i=1, ineq i_{1},...,i_{m-k+1} }<br /> x_{i}-sum^{m-k+1}_{ r=1} x_{i_{r}})\& hspace {2.8cm}+f(sum^{m}_{ i=1} x_{i})<br />-2^{m-1} f(x_{1})=0<br />end{align*}<br />where $m geq 2$ is an integer number.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160206Coupled coincidence point in ordered cone metric spaces with examples in game theory18319430510.22075/ijnaa.2015.305ENAlirezaNaeimi SadighDepartment of Mathematics, Statistics and Computer science, Semnan University, P.O. Box 35195-363, Semnan, IranSamanehGhodsDepartment of Mathematics, Islamic Azad University, Semnan Branch, Semnan, IranJournal Article20141208In this paper, we prove some coupled coincidence point theorems for mappings with the mixed monotone property and obtain the uniqueness of this coincidence point. Then we providing useful examples in Nash equilibrium.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160325On a class of paracontact Riemannian manifold19520530610.22075/ijnaa.2015.306ENMahmoodParchetalabDepartment of Mathematics, Faculty of Science, Arak university, Arak 38156-8-8349, IranJournal Article20150128We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160226Existence of solution and solving the integro-differential equations system by the multi-wavelet Petrov-Galerkin method20721830710.22075/ijnaa.2015.307ENMohsenRabbaniDepartment of Mathematics, Sari Branch, Islamic Azad University, Sari, IranJournal Article20141203In this paper, we discuss about existence of solution for integro-differential system and then we solve it by using the Petrov-Galerkin method. In the Petrov-Galerkin method choosing the trial and test space is important, so we use Alpert multi-wavelet as basis functions for these spaces. Orthonormality is one of the properties of Alpert multi-wavelet which helps us to reduce computations in the process of discretizing and we drive a system of algebraic equations with small dimension which it leads to approximate solution with high accuracy. We compare the results with similar works and it guarantees the validity and applicability of this method.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160305On fixed points of fundamentally nonexpansive mappings in Banach spaces21922430810.22075/ijnaa.2015.308ENMohammadMoosaeiDepartment of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, IranJournal Article20150128We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and convex, then its the fixed points set is nonempty, closed and convex.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160212Common fixed point of multivalued graph contraction in metric spaces22523030910.22075/ijnaa.2015.309ENMasoudHadian DehkordiDepartment of Mathematics, Faculty
of Basic Science,Iran University of Science and Technology, Narmak, Tehran,IranMasoudGhodsDepartment of Mathematics, Faculty
of Basic Science,Iran University of Science and Technology, Narmak, Tehran,IranJournal Article20141130In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $F,T$ be two multivalued mappings on $X.$ Among other things, we obtain a common fixed point of the mappings $F,T$ in the metric space $X$ endowed with a graph $G.$Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160408Dynamical behavior of a stage structured prey-predator model23124131110.22075/ijnaa.2015.311ENShashiKantDepartment of Applied Mathematics, Delhi Technological University, Delhi 110042, IndiaVivekKumarDepartment of Applied Mathematics, Delhi Technological University, Delhi 110042, IndiaJournal Article20150108In this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. The stages for prey have been considered. The proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. The model is analyzed by using linear stability analysis to obtain the conditions for which our model exhibits stability around the possible equilibrium points. Besides this a rigorous global stability analysis has been performed for our proposed model by using Li and Muldowney approach (geometric approach). Global stability conditions for the proposed model are described in the form of theorem. This is not a case study, hence the real parameters are not available for this model. However, model may be simulated by using hypothetical set of parameters. Investigation of real parameters for the proposed model is an open problem.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160104An analog of Titchmarsh's theorem for the Bessel transform in the space $mathrm{L}_{p,alpha}(mathbb{R}_{+})$24324831210.22075/ijnaa.2015.312ENMohamedEl HammaDepartment of Mathematics, Faculty of Sciences A"{i}n Chock,
University of Hassan II, BP 5366, Maarif, Casablanca, MoroccoR.DaherDepartment of Mathematics, Faculty of Sciences A"{i}n Chock,
University of Hassan II, BP 5366, Maarif, Casablanca, MoroccoM.BoujeddaineDepartment of Mathematics and Computer Sciences, Faculty of Sciences,
Equipe d'Analyse Harmonique et Probabilit'{e}s, Universit'{e} Moulay Isma"{i}l.
BP 11201 , Zitoune, Mekn`{e}s, MoroccoJournal Article20140523Using a Bessel generalized translation, we obtain an analog of Titchmarsh's theorem for the Bessel transform for functions satisfying the Lipschitz condition in the space $mathrm{L}_{p,alpha}(mathbb{R}_{+})$, where $alpha>-frac{1}{2}$ and $1<pleq 2$.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160408On a Hardy-Hilbert-Type Inequality with a General Homogeneous Kernel24926932310.22075/ijnaa.2015.323ENMichael 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, USABichengYangDepartment of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. ChinaJournal Article20150607By the method of weight coefficients and techniques of real analysis, a Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. The equivalent forms, the operator expressions with the norm, the reverses and some particular examples are also considered.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160501On the shadowing property of nonautonomous discrete systems27127729110.22075/ijnaa.2015.291ENHosseinRasuoliYoung Researchers and Elite Club, Malayer Branch, Azad University, Malayer, IranJournal Article20141013In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e. nonautonomous discrete dynamical systems. We investigate the relation of weak contractions with shadowing and h-shadowing property.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160218Regularized fractional derivatives in Colombeau algebra27928714710.22075/ijnaa.2015.147ENMohsenAlimohammadyDepartment of Mathematics, University of Mazandaran, Babolsar, IranFaribaFattahi AmirdehiDepartment of mathematics, University of Mazandaran, babolsar, IranJournal Article20140319The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to a nonlinear heat equation illustrating the application of the theory.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160428Functionally closed sets and functionally convex sets in real Banach spaces28929434010.22075/ijnaa.2015.340ENMadjidEshaghiDepartment of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranHamidrezaReisi DezakiDepartment of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranAlirezaMoazzenKosar University of Bojnord, Bojnord, IranJournal Article20150519Let $X$ be a real normed space, then $C(subseteq X)$ is functionally convex (briefly, $F$-convex), if $T(C)subseteq Bbb R $ is convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$ is functionally closed (briefly, $F$-closed), if $T(K)subseteq Bbb R $ is closed for all bounded linear transformations $Tin B(X,R)$. We improve the Krein-Milman theorem on finite dimensional spaces. We partially prove the Chebyshev 60 years old open problem. Finally, we introduce the notion of functionally convex functions. The function $f$ on $X$ is functionally convex (briefly, $F$-convex) if epi $f$ is a $F$-convex subset of $Xtimes mathbb{R}$. We show that every function $f : (a,b)longrightarrow mathbb{R}$ which has no vertical asymptote is $F$-convex.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160404On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings29530034110.22075/ijnaa.2015.341ENAliFarajzadehDepartment of Mathematics, Razi University, Kermanshah, IranJournal Article20150303In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [On fixed point theorems for monotone increasing vector valued mappings via scalarizing, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixed point, relaxation of the relatively compactness and the continuity on the map with replacing topological interior of the cone by the algebraic interior. Moreover, by applying Ascoli-Arzela's theorem an example in order to show that the main theorem of the paper [An intermediate value theorem for monotone operators in ordered Banach spaces, Fixed point theory and applications, 2012 (1) (2012) 1-4] may fail, is established.Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160601Completely continuous Banach algebras30130838310.22075/ijnaa.2016.383ENBahmanHayatiDepartment of Mathematics, Malayer University, P.O. Box 16846-13114, Malayer, Iran0000-0002-6283-3935Journal Article20150417 For a Banach algebra $mathfrak{A}$, we introduce ~$c.c(mathfrak{A})$, the set of all $phiin mathfrak{A}^*$ such that $theta_phi:mathfrak{A}to mathfrak{A}^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain mathfrak{A}$. We call $mathfrak{A}$, a completely continuous Banach algebra if $c.c(mathfrak{A})=mathfrak{A}^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an open problem raised for the first time by J.E Gale, T.J. Ransford and M. C. White: Is there exist an infinite dimensional amenable Banach algebra whose underlying Banach space is reflexive? We prove that a reflexive, amenable, completely continuous Banach algebra with the approximation property is trivial.