2015
7
1
1
0
Relative order and type of entire functions represented by Banach valued Dirichlet series in two variables
2
2
In 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.
1

1
14


Dibyendu
Banerjee
Department of Mathematics, VisvaBharati, Santiniketan 731235, India
Department of Mathematics, VisvaBharati,
Iran
dibyendu192@rediffmail.com


Nilkanta
Mondal
Ballavpur R.G.S.Vidyapith, Ballavpur713323, Raniganj, India
Ballavpur R.G.S.Vidyapith, Ballavpur713323,
Iran
nilkanta1986@gmail.com
Banach valued Dirichlet series
relative order
relative type
Entire function
On the quadratic support of strongly convex functions
2
2
In 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.
1

15
20


S.
Abbaszadeh
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195363, Iran
Department of Mathematics, Faculty of Mathematics,
Iran
s.abbaszadeh.math@gmail.com


M
Eshaghi Gordji
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195363, Iran
Department of Mathematics, Faculty of Mathematics,
Iran
madjid.eshgahi@gmail.com
strongly convex function
HahnBanach theorem
$c$affine functions
quadratic support
Nonexpansive mappings on complex C*algebras and their fixed points
2
2
A 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}^star$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}^star$algebra (not necessarily commutative), then $ A $ does not have the fixed point property.
1

21
29


Davood
Alimohammadi
Department of Mathematics, Faculty of Science, Arak university, Arak 3815688349, Iran
Department of Mathematics, Faculty of Science,
Iran
alimohammadi.davood@gmail.com
Banach space
C*algebra
Fixed point property
Nonexpansive mapping
normed linear space
On the fine spectrum of generalized upper triangular doubleband matrices $Delta^{uv}$ over the sequence spaces $c_o$ and $c$
2
2
The main purpose of this paper is to determine the fine spectrum of the generalized upper triangular doubleband matrices uv over the sequence spaces c0 and c. These results are more general than the spectrum of upper triangular doubleband matrices of Karakaya and Altun[V. Karakaya, M. Altun, Fine spectra of upper triangular doubleband matrices, Journal of Computational and Applied Mathematics, 234(2010) 13871394].
1

31
43


Javad
Fathi
Department of Mathematic, Faculty of Science, Hormozgan University, Bandarabbas, Iran
Department of Mathematic, Faculty of Science,
Iran
jfathij@yahoo.com
Spectrum of an operator
matrix mapping
sequence space
Common fixed point theorem for nonexpansive type single valued mappings
2
2
The 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) 330339].
1

45
51


Pankaj
Jhade
NRI Institute of Information Science & Technology, Bhopal, MP, INDIA462021
NRI Institute of Information Science &
Iran
pmathsjhade@gmail.com


A S
Saluja
J H Govt. PG College, Betul India460001
J H Govt. PG College, Betul India460001
Iran
dssaluja@rediffmail.com
Nonexpansive mapping
Common fixed point
reciprocal continuous
weak reciprocal continuous
Some fixed point theorems for weakly subsequentially continuous and compatible of type (E) mappings with an application
2
2
In this paper, we will establish some xed 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.
1

53
62


Said
Beloul
University of Eloued (Algeria)
University of Eloued (Algeria)
Iran
beloulsaid@gmail.com
generalized contractive condition
weakly subsequentially continuous
compatible of type (E)
functional equation
Approximate a quadratic mapping in multiBanach spaces, a fixed point approach
2
2
Using the fixed point method, we prove the generalized HyersUlamRassias stability of the following functional equation in multiBanach spaces:begin{equation} sum_{ j = 1}^{n}fBig(2 x_{j} + sum_{ i = 1, ineq j}^{n} x_{i}Big) =(n6) fBig(sum_{ i = 1}^{n} x_{i}Big) + 9 sum_{ i = 1}^{n}f(x_{i}).end{equation}
1

63
75


Sattar
Alizadeh
Marand Branch, Islamic Azad University,
Marand Branch, Islamic Azad University,
Iran
alizades_ms@yahoo.com


Fridoun
Moradlou
Department of Mathematics, Sahand University of Technology, Tabriz, Iran
Department of Mathematics, Sahand University
Iran
fridoun.moradlou@gmail.com
Fixed point method, HyersUlamRassias stability
MultiBanach spaces, Quadratic mapping
On the generalization of Trapezoid Inequality for functions of two variables with bounded variation and applications
2
2
In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.
1

77
85


Huseyin
Budak
Department of Mathematics, Faculty of Science and Arts, D"{u}zce University, D"{u}zceTurkey
Department of Mathematics, Faculty of Science
Iran
hsyn.budak@gmail.com


Mehmet
Sarikaya
Department of Mathematics, Faculty of Science and Arts, D"{u}zce University, D"{u}zceTurkey
Department of Mathematics, Faculty of Science
Iran
sarikayamz@gmail.com
Bounded Variation
Ostrowski type inequalities
RiemannStieltjes
Trapezoid Inequality
Generalized solution of SineGordon equation
2
2
In this paper, we are interested to study the SineGordon 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.
1

87
92


Lalla Saadia
Chadli
Sultan Moulay Slimane University
Sultan Moulay Slimane University
Iran
chadli@fstbm.ac.ma


Said
Melliani
Sultan Moulay Slimane University
Sultan Moulay Slimane University
Iran
saidmelliani@gmail.com


Abdelaziz
Moujahid
Sultan Moulay Slimane University
Sultan Moulay Slimane University
Iran
same@fstbm.ac.ma


Mhamed
Elomari
Sultan Moulay Slimane University
Sultan Moulay Slimane University
Iran
mhamedmaster@gmail.com
Algebra Colombeau
Generalized functions theory
SineGordon equation
Titchmarsh theorem for Jacobi DiniLipshitz functions
2
2
Our 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 DiniLipschitz 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 DiniLipschitz condition in $L^{p}$.
1

93
101


Mustapha
Boujeddaine
Department of Mathematics and Computer Sciences, Faculty of Sciences,
Equipe d'Analyse Harmonique et Probabilites, Universite Moulay Ismal,
BP 11201 Zitoune, Meknes, Morocco
Department of Mathematics and Computer Sciences,
Iran
boujeddainemustapha@gmail.com


Said
Fahlaoui
Department of Mathematics and Computer Sciences, Faculty of Sciences,
Equipe d'Analyse Harmonique et Probabilites, Universite Moulay Ismal,
BP 11201 Zitoune, Meknes, Morocco
Department of Mathematics and Computer Sciences,
Iran
saidfahlaoui@gmail.com


Radouan
Daher
Department of Mathematics, Faculty of Sciences An Chock,
University of Hassan II, BP 5366, Maarif, Casablanca, Morocco
Department of Mathematics, Faculty of Sciences
Iran
rjdaher024@gmail.com
DiniLipschitz functions
Jacobi operator
Jacobi transform
Some new results using Hadamard fractional integral
2
2
Fractional 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.
1

103
109


Sabrina
Taf
Department of Mathematic, Faculty SEI, UMAB University of Mostaganem, Algeria
Department of Mathematic, Faculty SEI, UMAB
Iran
sabrina481@hotmail.fr


Kamel
Brahim
Faculty of science of Tunis, Tunisia
Faculty of science of Tunis, Tunisia
Iran
kamel.brahim@ipeit.rnu.tn
Hadamard fractional integral
Fractional integral inequalities
Minkowski's inequality
Some common fixed point theorems for four $(psi,varphi)$weakly contractive mappings satisfying rational expressions in ordered partial metric spaces
2
2
The 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 wellknown results in the literature. Also, we give two examples to illustrate our results.
1

111
130


R.A.
Rashwan
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Department of Mathematics, Faculty of Science,
Iran
rr_rashwan54@yahoo.com


S.M.
Saleh
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Department of Mathematics, Faculty of Science,
Iran
samirasaleh2007@yahoo.com
Common fixed point
rational contractions
ordered partial metric spaces
dominating and dominated mappings
A determinant inequality and logmajorisation for operators
2
2
Let $lambda_1,dots,lambda_n$ 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 $t(1)<infty$, $$prod_{k=1}^n(det a_k)^{lambda_k},le,det (sum_{k=1}^n lambda_k a_k),$$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$, then equality holds if and only if $a_1=a_2=cdots =a_n$. A logmajorisation version of Young inequality are given as well.
1

131
140


Seyed Mahmoud
Manjegani
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 8415683111
Department of Mathematical Sciences, Isfahan
Iran
manjgani@cc.iut.ac.ir
Singular values
Semifinite trace
Majorisation
logmajorisation
On the $s^{th}$ derivative of a polynomial
2
2
For 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 $(ns)$. 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 wellknown results.
1

141
145


Abdullah
Mir
Department of Mathematics, University of Kashmir, Srinagar, $190006$, (India)
Department of Mathematics, University of
Iran
mabdullah_mir@yahoo.co.in
Polynomial
Zeros
$s^{th}$ derivative
Vector ultrametric spaces and a fixed point theorem for correspondences
2
2
In 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.
1

147
153


Kourosh
Nourouzi
Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 163151618, Tehran, Iran
Faculty of Mathematics, K.N. Toosi University
Iran
nourouzi@kntu.ac.ir
Vector ultra metric space
Correspondence
fixed point
Variational inequalities on Hilbert $C^*$modules
2
2
We 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.
1

155
165


Hedayat
Fathi
Department of Mathematics, Shahid Beheshti University, Tehran, Iran
Department of Mathematics, Shahid Beheshti
Iran
hedayat.fathi@yahoo.com


S.A.R.
Hosseinioun
Department of Mathematics, Shahid Beheshti University, Tehran, Iran;
Department of Mathematics, University of Arkansas,
Fayetteville, Arkansas 72701, USA
Department of Mathematics, Shahid Beheshti
Iran
ahosseinioun@yahoo.com
variational inequality
Hilbert $C^*$module
metric projection
fixed point
Approximately generalized additive functions in several variables via fixed point method
2
2
In this paper, we obtain the general solution and the generalized HyersUlamRassias stability in random normed spaces, in nonArchimedean spaces and also in $p$Banach spaces and finally the stability via fixed point method for a functional equationbegin{align*}&D_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{mk+1}=i_{mk}+1}) f(sum^{m}_{i=1, ineq i_{1},...,i_{mk+1} } x_{i}sum^{mk+1}_{ r=1} x_{i_{r}})\& hspace {2.8cm}+f(sum^{m}_{ i=1} x_{i})2^{m1} f(x_{1})=0end{align*}where $m geq 2$ is an integer number.
1

167
181


R.
Farokhzad Rostami
Department of Mathematics, Gonbad Kavous University, Gonbad Kavous, Golestan, Iran
Department of Mathematics, Gonbad Kavous
Iran
razieh.farokhzad@yahoo.com


S.A.R.
Hoseinioun
Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USA
Department of Mathematical Sciences, University
Iran
ahosseinioun@yahoo.com
Additive function
$p$Banach spaces
Random normed spaces
NonArchimedean spaces
Fixed point method
generalized HyersUlam stability
Coupled coincidence point in ordered cone metric spaces with examples in game theory
2
2
In 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.
1

183
194


Alireza
Naeimi Sadigh
Department of Mathematics, Statistics and Computer science, Semnan University, P.O. Box 35195363, Semnan, Iran
Department of Mathematics, Statistics and
Iran
anaeimi@gmail.com


Samaneh
Ghods
Department of Mathematics, Islamic Azad University, Semnan Branch, Semnan, Iran
Department of Mathematics, Islamic Azad University
Iran
s1ghods@gmail.com
Coupled fixed point
Coupled coincidence Fixed point
Partially ordered sets
Cone metric space
Game theory
Nash equilibrium
On a class of paracontact Riemannian manifold
2
2
We 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 semisymmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.
1

195
205


Mahmood
Parchetalab
Department of Mathematics, Faculty of Science, Arak university, Arak 3815688349, Iran
Department of Mathematics, Faculty of Science,
Iran
mparchetalab@araku.ac.ir
paracontact structure
Einstein structure
parasasakian
Existence of solution and solving the integrodifferential equations system by the multiwavelet PetrovGalerkin method
2
2
In this paper, we discuss about existence of solution for integrodifferential system and then we solve it by using the PetrovGalerkin method. In the PetrovGalerkin method choosing the trial and test space is important, so we use Alpert multiwavelet as basis functions for these spaces. Orthonormality is one of the properties of Alpert multiwavelet 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.
1

207
218


Mohsen
Rabbani
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mathematics, Sari Branch, Islamic
Iran
mrabbani@iust.ac.ir
System of Integrodifferential equations
Multiwavelet
PetrovGalerkin
Regular pairs
Trial space
Test space
On fixed points of fundamentally nonexpansive mappings in Banach spaces
2
2
We first obtain some properties of a fundamentally nonexpansive selfmapping 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.
1

219
224


Mohammad
Moosaei
Department of Mathematics, Faculty of Science, BuAli Sina University, Hamedan, Iran
Department of Mathematics, Faculty of Science,
Iran
m.moosaei@basu.ac.ir
fixed point
fundamentally nonexpansive mappings
nonexpansive mappings
Opial's condition
uniformly convex Banach spaces
Common fixed point of multivalued graph contraction in metric spaces
2
2
In 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 $G.$
1

225
230


Masoud
Hadian Dehkordi
Department of Mathematics, Faculty
of Basic Science,Iran University of Science and Technology, Narmak, Tehran,Iran
Department of Mathematics, Faculty
of Basic
Iran
mhadian@iust.ac.ir


Masoud
Ghods
Department of Mathematics, Faculty
of Basic Science,Iran University of Science and Technology, Narmak, Tehran,Iran
Department of Mathematics, Faculty
of Basic
Iran
mghods@iust.ac.ir
fixed point
multivalued
common(G$psi$) contraction
directed graph
Dynamical behavior of a stage structured preypredator model
2
2
In this paper, a new stage structured preypredator 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.
1

231
241


Shashi
Kant
Department of Applied Mathematics, Delhi Technological University, Delhi 110042, India
Department of Applied Mathematics, Delhi
Iran
onlineskmishra@gmail.com


Vivek
Kumar
Department of Applied Mathematics, Delhi Technological University, Delhi 110042, India
Department of Applied Mathematics, Delhi
Iran
vivekumar@gmail.com
Stage Structured Population
Global Stability
Local Stability
An analog of Titchmarsh's theorem for the Bessel transform in the space $mathrm{L}_{p,alpha}(mathbb{R}_{+})$
2
2
Using 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 $1<pleq 2$.
1

243
248


Mohamed
El Hamma
Department of Mathematics, Faculty of Sciences A"{i}n Chock,
University of Hassan II, BP 5366, Maarif, Casablanca, Morocco
Department of Mathematics, Faculty of Sciences
Iran
m_elhamma@yahoo.fr


R.
Daher
Department of Mathematics, Faculty of Sciences A"{i}n Chock,
University of Hassan II, BP 5366, Maarif, Casablanca, Morocco
Department of Mathematics, Faculty of Sciences
Iran
rjdaher024@gmail.com


M.
Boujeddaine
Department 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, Morocco
Department of Mathematics and Computer Sciences,
Iran
boujeddainemustapha@gmail.com
Bessel operator
Bessel transform
Bessel generalized translation
On a HardyHilbertType Inequality with a General Homogeneous Kernel
2
2
By the method of weight coefficients and techniques of real analysis, a HardyHilberttype 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.
1

249
269


Michael Th.
Rassias
Institute of Mathematics, University of Zurich, CH  8057, Zurich, Switzerland & Institute for Advanced Study, Program in Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ 08540, USA
Institute of Mathematics, University of Zurich,
Iran
michailrassias@math.princeton.edu


Bicheng
Yang
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
Department of Mathematics, Guangdong University
Iran
bcyang@gdei.edu.cn
HardyHilberttype inequality, weight coefficient, equivalent form, reverse
operator
On the shadowing property of nonautonomous discrete systems
2
2
In 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 hshadowing property.
1

271
277


Hossein
Rasuoli
Young Researchers and Elite Club, Malayer Branch, Azad University, Malayer, Iran
Young Researchers and Elite Club, Malayer
Iran
hoseinrasuli@yahoo.com
Nonautonomous discrete system
nonautonomos difference equation
shadowing property
Regularized fractional derivatives in Colombeau algebra
2
2
The 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.
1

279
287


Mohsen
Alimohammady
Department of Mathematics, University of Mazandaran, Babolsar, Iran
Department of Mathematics, University of
Iran
amohsen@umz.ac.ir


Fariba
Fattahi Amirdehi
Department of mathematics, University of Mazandaran, babolsar, Iran
Department of mathematics, University of
Iran
fariba.fattahi30@gmail.com
Functionally closed sets and functionally convex sets in real Banach spaces
2
2
Let $X$ 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 KreinMilman 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.
1

289
294


Madjid
Eshaghi
Department of Mathematics, Semnan University, P.O. Box 35195363, Semnan, Iran
Department of Mathematics, Semnan University,
Iran
madjid.eshaghi@gmail.com


Hamidreza
Reisi Dezaki
Department of Mathematics, Semnan University, P.O. Box 35195363, Semnan, Iran
Department of Mathematics, Semnan University,
Iran
hamidreza.reisi@gmail.com


Alireza
Moazzen
Kosar University of Bojnord, Bojnord, Iran
Kosar University of Bojnord, Bojnord, Iran
Iran
ar.moazzen@yahoo.com
Convex set
Chebyshev set
KreinMilman theorem
On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings
2
2
In 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 [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333340] 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 AscoliArzela's theorem an example in order to show that the main theorem of the paper [textit{An intermediate value theorem for monotone operators in ordered Banach spaces}, Fixed point theory and applications, 2012 (1) (2012) 14] may fail, is established.
1

295
300


Ali
Farajzadeh
Department of Mathematics, Razi University, Kermanshah
Department of Mathematics, Razi University,
Iran
farajzadehali@gmail.com
intermediate value theorem
fixed point
increasing mapping
algebraic interior
normal cone
Completely continuous Banach algebras
2
2
For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. 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 Gal`{e}, 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.
1

301
308


Bahman
Hayati
Department of Mathematics, Malayer University, P.O. Box 1684613114, Malayer, Iran
Department of Mathematics, Malayer University,
Iran
bahmanhayati@yahoo.com
amenability
Completely continuous
Banach algebra