University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101On Some Properties of the Max Algebra System Over Tensors1143002310.22130/scma.2018.30023ENAli Reza ShojaeifardDepartment of Mathematics and Statistics, Faculty of Basic Sciences, Imam Hossein Comprehensive University, Tehran, Iran.Hamid Reza AfshinDepartment of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Islamic Republic of Iran.Journal Article20170406Recently we generalized the max algebra system to the class of nonnegative tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and investigate its properties relevant to the spectral theory.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101Inequality Problems of Equilibrium Problems with Application15263086010.22130/scma.2018.46703.100ENAyed Eleiwis HashooshDepartment of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq.Mohsen AlimohammadyDepartment of mathematics, University of Mazandaran, Babolsar, Iran.Haiffa Mohsen BuiteDepartment of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq.Journal Article20160805This paper aims at establishing the existence of results for a nonstandard equilibrium problems $(EP_{N})$. The solutions of this inequality are discussed in a subset $K$ (either bounded or unbounded) of a Banach spaces $X$. Moreover, we enhance the main results by application of some differential inclusion.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101On Regular Generalized $delta$-closed Sets in Topological Spaces27373167010.22130/scma.2018.67135.257ENSomasundaram RajakumarDepartment of Science and Humanities, Krishnasamy College of Engineering and Technology, Cuddalore, Tamil Nadu-608 002, India.Journal Article20170629In this paper a new class of sets called regular generalized $delta$-closed set (briefly rg$delta$-closed set)is introduced and its properties are studied. Several examples are provided to illustrate the behaviour of these new class of sets.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent39573080210.22130/scma.2018.46462.98ENSomayeh KhademlooDepartment of Basic Sciences, Babol Noushirvani University of Technology, 47148-71167, Babol, Iran.Saeed Khanjany GhaziDepartment of Basic Sciences, Babol Noushirvani University of Technology, 47148-71167, Babol, Iran.Journal Article20160731In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101$(-1)$-Weak Amenability of Second Dual of Real Banach Algebras59883411310.22130/scma.2018.88929.466ENHamidreza AlihoseiniDepartment of Mathematics, Faculty of Science, University of Arak, 38156-8-8349, Arak, Iran.Davood AlimohammadiDepartment of Mathematics, Faculty of Science, University of Arak, 38156-8-8349, Arak, Iran.Journal Article20180630Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on $ A_mathbb{C} $ satisfying a simple condition together with the norm $ | cdot | $ on $ A$. In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{**}$-module. Next we prove that $ A^{**} $ is $ (-1)$-weakly amenable if and only if $ (A_mathbb{C})^{**} $ is $ (-1)$-weakly amenable. Finally, we give some examples of real Banach algebras which their second duals of some them are and of others are not $ (-1)$-weakly amenable.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101The Norm Estimates of Pre-Schwarzian Derivatives of Spirallike Functions and Uniformly Convex $alpha$-spirallike Functions89963136110.22130/scma.2018.68371.262ENZahra OroujiDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.Rasul AghalaryDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.Journal Article20170718For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$, we define<br />a subclass of the spirallike functions, $SP_{p}(alpha)$, the set<br />of all functions $fin mathcal{A}$<br />[<br />releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.<br />]<br />In the present paper, we shall give the estimate of the<br /> norm of the pre-Schwarzian derivative $mathrm{T}_f=f''/f'$ where $|mathrm{T}_f|=sup_{zin Delta} (1-|z|^2)|mathrm{T}_f(z)|$ for the functions in $SP_{p}(alpha)$.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101Numerical Reckoning Fixed Points in $CAT(0)$ Spaces971113417910.22130/scma.2018.62911.238ENKifayat UllahDepartment of Mathematics, University of Science and Technology
Bannu, KPK Pakistan.Hikmat KhanDepartment of Mathematics, University of Science and Technology Bannu, KPK Pakistan.Muhammad ArshadDepartment of Mathematics, International Islamic University, H-10, Islamabad - 44000, Pakistan.Journal Article20170427In this paper, first we use an example to show the efficiency of $M$ iteration process introduced by Ullah and Arshad [4] for approximating fixed points of Suzuki generalized nonexpansive mappings. Then by using $M$ iteration process, we prove some strong and $Delta -$convergence theorems for Suzuki generalized nonexpansive mappings in the setting of $CAT(0)$ Spaces. Our results are the extension, improvement and generalization of many known results in $CAT(0)$ spaces.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101A Certain Class of Character Module Homomorphisms on Normed Algebras1131203119910.22130/scma.2018.78500.364ENAli Reza KhoddamiFaculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box 3619995161-316, Shahrood, Iran.Journal Article20180101For two normed algebras $A$ and $B$ with the character space $bigtriangleup(B)neq emptyset$ and a left $B-$module $X,$ a certain class of bounded linear maps from $A$ into $X$ is introduced. We set $CMH_B(A, X)$ as the set of all non-zero $B-$character module homomorphisms from $A$ into $X$. In the case where $bigtriangleup(B)=lbrace varphirbrace$ then $CMH_B(A, X)bigcup lbrace 0rbrace$ is a closed subspace of $L(A, X)$ of all bounded linear operators from $A$ into $X$. We define an equivalence relation on $CMH_B(A, X)$ and use it to show that $CMH_B(A, X)bigcuplbrace 0rbrace $ is a union of closed subspaces of $L(A, X)$. Also some basic results and some hereditary properties are presented. Finally some relations between $varphi-$amenable Banach algebras and character module homomorphisms are examined.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101$L^p$-Conjecture on Hypergroups1211303138610.22130/scma.2018.66851.256ENSeyyed Mohammad TabatabaieDepartment of Mathematics, University of Qom, Qom 3716146611, Iran.Faranak HaghighifarDepartment of Mathematics, University of Qom, Qom 3716146611, Iran.Journal Article20170624In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions for a weighted Lebesgue space $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$. Among the other things, we also show that if $K$ is a locally compact hypergroup and $p$ is greater than 2, $K$ is compact if and only if $m(K)$ is finite and $fast g$ exists for all $f,gin L^p(K)$, where $m$ is a left Haar measure for $K$, and in particular, if $K$ is discrete, $K$ is finite if and only if the convolution of any two elements of $L^p(K)$ exists.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101On Fuzzy $e$-open Sets, Fuzzy $e$-continuity and Fuzzy $e$-compactness in Intuitionistic Fuzzy Topological Spaces1311532822310.22130/scma.2017.28223ENVeerappan ChandrasekarDepartment of Mathematics, Kandaswami Kandar's College, P-velur-638 182, Tamil Nadu, India.Durairaj SobanaDepartment of Mathematics, Kandaswami Kandar's College, P-velur-638 182, Tamil Nadu, India.Appachi VadivelDepartment of Mathematics, Annamalai University, Annamalainagar, Tamil Nadu-608 002.Journal Article20170108The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results related topological concepts. Several preservation properties and some characterizations concerning intuitionistic fuzzy $e$-compactness have been obtained.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101On Generators in Archimedean Copulas1551662840110.22130/scma.2017.28401ENVadoud NajjariYoung Researchers and Elite Club, Maragheh branch, Islamic Azad University, Maragheh, Iran.Journal Article20170206This study after reviewing construction methods of generators in Archimedean copulas (AC), proposes several useful lemmas related with generators of AC. Then a new trigonometric Archimedean family will be shown which is based on cotangent function. The generated new family is able to model the low dependence structures.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101Some Properties of Reproducing Kernel Banach and Hilbert Spaces1671772782210.22130/scma.2017.27822ENSaeed Hashemi SababeDepartment of Mathematics, Payame Noor University (PNU), P.O. Box, 19395-3697, Tehran, Iran.0000-0003-1167-5006Ali EbadianDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.Journal Article20161022This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels and prove some theorems in this subject.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101On Some Results in the Light of Generalized Relative Ritt Order of Entire Functions Represented by Vector Valued Dirichlet Series1791862364710.22130/scma.2017.23647ENSanjib Kumar DattaDepartment of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.Tanmay BiswasRajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.Journal Article20160625In this paper, we study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of generalized relative Ritt order and generalized relative Ritt lower order.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101On Character Space of the Algebra of BSE-functions1871942798210.22130/scma.2017.27982ENMohammad FozouniDepartment of Mathematics and Statistics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University, P.O.Box 163, Gonbad Kavous, Iran.Journal Article20161031Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterization of $Delta(C_{rm{BSE}}(Delta(A)))$ and in the general case we give a partial answer. Also, using the Fourier algebra, we show that $C_{rm{BSE}}(Delta(A))$ is not a $C^*$-algebra in general. Finally for some subsets $E$ of $A^*$, we define the subspace of BSE-like functions on $Delta(A)cup E$ and give a nice application of this space related to Goldstine's theorem.University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101A New Approach to Nonstandard Analysis1952543418710.22130/scma.2018.63978.244ENSaghe AbdeljalilCpge de Settat, Lycee Qualifiant Technique PB: 576-Maroc.Journal Article20170513In this paper, we propose a new approach to nonstandard analysis without using the ultrafilters. This method is very simple in practice. Moreover, we construct explicitly the total order relation in the new field of the infinitesimal numbers. To illustrate the importance of this work, we suggest comparing a few applications of this approach with the former methods.