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, (...

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, (...

‎Let $\Omega_X$ be a bounded‎, ‎circular and strictly convex domain in a complex Banach space $X$‎, ‎and $\mathcal{H}(\Omega_X)$ be the space of all holomorphic functions from $\Omega_X$ to $\mathbb{C}$‎. ‎The growth space $\mathcal{A}^\nu(\Omega_X)$ consists of all $f\in\mathcal{H}(\Omega_X)$‎ ‎such that $$|f(x)|\leqslant C \nu(r_{\Omega_X}(x)),\quad x\in \Omega_X,$$‎ ‎for some constant $C>0$‎...

Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.

We force a first countable, normal, locally compact, initially ω1-compact but non-compact space X of size ω2. The onepoint compactification of X is a non-first countable compactum without any (non-trivial) converging ω1-sequence.

‎This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...

 In this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. We extract the information function ofan ergodic dynamical system (X,T) from the relative information of T fromthe view point of observer χX, where X denotes the base space of the system.We also generalize the in...

Let $(X,d)$ be a compactmetric space and let $K$ be a nonempty compact subset of $X$. Let $alpha in (0, 1]$ and let ${rm Lip}(X,K,d^ alpha)$ denote the Banach algebra of all  continuous complex-valued functions $f$ on$X$ for which$$p_{(K,d^alpha)}(f)=sup{frac{|f(x)-f(y)|}{d^alpha(x,y)} : x,yin K , xneq y}

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.