In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:Crightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we ...

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, (...

We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions. Keywords—sequentially locally non-constant functions, Tychonoff’s fixed point theorem, constructive mathematics.

The eggshell of the hen is a highly ordered and mineralised structure, which is sequentially deposited within an acellular milieu – the uterine fluid secreted by the distal oviduct. Spherulitic crystal growth of calcite is initiated on organic aggregates on surface of the eggshell membranes, followed by competition between radial crystallites for space to form a compact columnar biomineral. The...

‎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.

Let {Pn} be a sequence of covers of a space X such that {st(x,Pn)} is a network at x inX for each x ∈ X. For each n ∈ N, let Pn = {Pβ : β ∈ Λn} and Λn be endowed the discrete topology. Put M = {b = (βn) ∈ Πn∈NΛn : {Pβn} forms a network at some point xb in X} and f : M −→ X by choosing f(b) = xb for each b ∈ M . In this paper, we prove that f is a sequentiallyquotient (resp. sequence-covering, c...