Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367220201101New Bounds for Entropy of Information Sourcesکران های جدید برای آنتروپی منبع های اطلاعات194666910.22072/wala.2020.111881.1240ENYaminSayyariDepartment of Mathematics, Sirjan University Of Technology, Sirjan, Islamic Republic of Iran.0000-0001-8019-3655Journal Article20190724Shannon's entropy plays an important role in information theory, dynamical systems and thermodynamics. In this paper we applying Jensen's inequality in information theory and we obtain some results for the Shannon's entropy of random variables and Shannon's entropy of stochastic process. Also we obtain upper bound and lower bound for Shannon's entropy of information sources.https://wala.vru.ac.ir/article_46669_dffe93f985ab86301115dfe29c3e0a41.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367220201101Some New Hermite-Hadamard Type Inequalities for Convex Functionsبرخی نامساوی های جدید از نوع نامساوی هرمیت-هادامارد برای توابع محدب11224667110.22072/wala.2020.117932.1260ENHasanBarsamDepartment of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Islamic Republic of Iran.Journal Article20191202Convex sets and convex functions play a fundamental role in the development of various fields <br />of pure and applied mathematics. Recently, many new generalizations of inequalities with respect to Hermite-Hadamard have been proposed in the literature. In this paper, some new inequalities of the Hermite-Hadamard type for differentiable convex functions are given. These new inequalities are based on the second derivative functions.https://wala.vru.ac.ir/article_46671_6079012e410176453cbb3274cfe14bac.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367220201101The Banach algebras with generalized matrix representationجبرهای باناخ دارای نمایش ماتریسی تعمیم یافته23294668910.22072/wala.2020.122402.1273ENS.BarootkoobDepartment of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Islamic Republic of Iran.Journal Article20200229A Banach algebra $\mathfrak{A}$ has a generalized Matrix representation if there exist the algebras $A, B$, $(A,B)$-module $M$ and $(B,A)$-module $N$ such that $\mathfrak{A}$ is isomorphic to the generalized matrix Banach algebra $\Big[\begin{array}{cc}<br />A & \ M \\<br />N & \ B%<br />\end{array}%<br />\Big]$.<br />In this paper, the algebras with generalized matrix representation will be characterized. Then we show that there is a unital permanently weakly amenable Banach algebra $A$ without generalized matrix representation such that $H^1(A,A)=\{0\}$.<br />This implies that there is a unital Banach algebra $A$ without any triangular matrix representation such that $H^1(A,A)=\{0\}$ and gives a negative answer to the open question of \cite{D}.https://wala.vru.ac.ir/article_46689_16d40a3be745187190a9683cc8a9e1c0.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367220201101Weak and cyclic amenability of certain function algebrasمیانگین پذیری ضعیف و دوری جبرهای تابعی خاص31414673010.22072/wala.2020.124774.1280ENAli RezaKhoddamiFaculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box
3619995161-316, Shahrood, Islamic Republic of Iran.Journal Article20200416We consider $C^{b\varphi}(K)$ to be the space $C^b(K)$ equipped with the product $f\cdot g=f\varphi g$ for all $f, g\in C^b(K)$ where, $K=\overline{B_1^{(0)}}$ is the closed unit ball of a non-zero normed vector space $A$ and $\varphi$ is a non-zero element of $A^*$ such that $\Vert \varphi \Vert\leq 1$. We define $\Vert f \Vert_\varphi=\Vert f\varphi \Vert_\infty$ for all $f\in C^{b\varphi}(K)$. Some relations between the dual spaces of $(C^{b\varphi}(K), \Vert \cdot \Vert_\infty)$ and $(C^{b\varphi}(K), \Vert \cdot \Vert_\varphi)$ are investigated. Also we characterize the derivations from $(C^{b\varphi}(K), \Vert \cdot \Vert_\infty)$ and $(C^{b\varphi}(K), \Vert \cdot \Vert_\varphi)$ into $(C^{b\varphi}(K), \Vert \cdot \Vert_\infty)^*$ and $(C^{b\varphi}(K), \Vert \cdot \Vert_\varphi)^*$ respectively. Finally we investigate the weak and cyclic amenability of $(C^{b\varphi}(K), \Vert \cdot \Vert_\infty)$ and $(C^{b\varphi}(K), \Vert \cdot \Vert_\varphi)$.https://wala.vru.ac.ir/article_46730_9e7dc95c541eb2d8bf26affe1089821f.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367220201101The structure of the set of all $C^*$-convex maps in $*$-ringsThe structure of the set of all C*-convex maps in *-rings43514673110.22072/wala.2020.125309.1282ENAliEbrahimi MeymandDepartment of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan,\\ Rafsanjan, Islamic Republic of Iran.Journal Article20200425In this paper, for every unital $*$-ring $\mathcal{S}$, we investigate the Jensen's inequality preserving maps on $C^*$-convex subsets of $\mathcal{S}$, which we call them $C^*$-convex maps on $\mathcal{S}$. We consider an involution for maps on $*$-rings, and we show that for every $C^*$-convex map $f$ on the $C^*$-convex set $B$ in $\mathcal{S}$, $f^*$ is also a $C^*$-convex map on $B$. We prove that in the unital commutative $*$-rings, the set of all $C^*$-convex maps ($C^*$-affine maps) on a $C^*$-convex set $B$, is also a $C^*$-convex set. In addition, we prove some results for increasing $C^*$-convex maps. Moreover, it is proved that the set of all $C^*$-affine maps on $B$, is a $C^*$-face of the set of all $C^*$-convex maps on $B$ in the unital commutative $*$-rings. Finally, some examples of $C^*$-convex maps and $C^*$-affine maps in $*$-rings are given.https://wala.vru.ac.ir/article_46731_f6aed15f2be438a3eb192c8ae3a1436c.pdf