Sahand Communications in Mathematical Analysis
Volume:17 Issue: 4, Autumn 2020

‎Let $A$ be a non-zero normed vector space and let $K=overline{B_1^{(0)}}$ be the closed unit ball of $A$. Also, let $varphi$ be a non-zero element of $ A^*$ such that $Vert varphi Vertleq 1$. We first define a new norm $Vert cdot Vert_varphi$ on $C^b(K)$, that is a non-complete, non-algebraic norm and also non-equivalent to the norm $Vert cdot Vert_infty$. We next show that for $0neqpsiin A^*$ with $Vert psi Vertleq 1$, the two norms  $Vert cdot Vert_varphi$ and $Vert cdot Vert_psi$ are equivalent if and only if $varphi$ and $psi$ are linearly dependent. Also by applying the norm $Vert cdot Vert_varphi $ and a new product `` $cdot$ '' on $C^b(K)$, we present the normed algebra $ left( C^{bvarphi}(K), Vert cdot Vert_varphi right)$. Finally we  investigate some relations between strongly zero-product preserving maps on $C^b(K)$ and $C^{bvarphi}(K)$.

Let $f$ and $g$ be analytic in the open unit disc and, for $alpha ,$ $beta geq 0$, letbegin{align*}Jleft( alpha ,beta ,f,gright) & =frac{zf^{prime }(z)}{f^{1-alpha}(z)g^{alpha }(z)}+beta left( 1+frac{zf^{prime prime }(z)}{f^{prime}(z)}right) -beta left( 1-alpha right) frac{zf^{prime }(z)}{f(z)} \& quad -alpha beta frac{zg^{prime }(z)}{g(z)}text{.}end{align*}The main aim of this paper is to study the class of analytic functions which map $Jleft( alpha ,beta ,f,gright) $ onto conic regions. Several interesting problems such as arc length, inclusion relationship, rate of growth of coefficient and Growth rate of Hankel determinant will be discussed.

In this paper, we introduce chaotic measure for discrete and continuous dynamical systems and study some properties of measure chaotic systems. Also relationship between chaotic measure, ergodic and expansive measures is investigated. Finally, we prove a new version of variational principle for chaotic measure.

‎Let $S$ be a (not necessarily commutative) Clifford semigroup with idempotent set $E$. In this paper, we show that the first (second) Hochschild cohomology group and the first (second) module cohomology group of  semigroup algbera $ell^1(S)$ with coefficients in $ell^infty(S)$ (and also  $ell^1(S)^{(2n-1)}$ for $nin mathbb{N}$) are equal.

In this study the main endeavor is to model dependence structure  between crude oil prices of West Texas Intermediate (WTI) and Brent - Europe.  The main activity is on concentrating copula technique which is powerful technique in modeling dependence structures.  Beside several well known Archimedean copulas, three new Archimedean families are used which have recently presented to the literature. Moreover, convex combination of these copulas also  are investigated on modeling of the mentioned dependence structure. Modeling process is relied on 318 data  which are average of the monthly prices from Jun-1992 to Oct-2018.

‎In this note, we study the integral operators $I_{g}^{gamma, alpha}$ and $J_{g}^{gamma, alpha}$ of an analytic function $g$ on convex and starlike functions of a complex order. Then, we investigate the same operators on $H^{infty}$ and Besov spaces.

In this paper, by making use of $(p , q) $-derivative operator we introduce a new subclass of meromorphically univalent functions. Precisely, we give a necessary and sufficient coefficient condition for functions in this class. Coefficient estimates, extreme points, convex linear combination, Radii of starlikeness and convexity and finally partial sum property are investigated.

In this work systems of sines $sin left(n+beta right)t,, , n=1,2, ldots,$ and cosines $cos left(n-beta right)t,, , n=0,1,2, ldots,$ are considered, where $beta in R-$is a real parameter. The subspace $M^{p,alpha } left(0,pi right)$ of the Morrey space $L^{p,alpha } left(0,pi right)$ in which continuous functions are dense is considered. Criterion   for the completeness, minimality and basicity of these systems with respect to the parameter $beta $  in the subspace  $M^{p,alpha } left(0,pi right)$, $1<p <+infty, $  are  found.

In this paper, some fixed point results of self mapping which is defined on orthogonal cone metric spaces are given by using extensions of orthogonal contractions. And by taking advantage of these results, the necessary conditions for self mappings on orthogonal cone metric space to have P property are investigated. Also an example is given to illustrate the main results.