New fixed point free nonexpansive maps on weakly compact, convex subsets of L1[0,1]

Common Fixed Point Theorems on Weakly Contractive and Nonexpansive Mappings

Uniform Convergence to a Left Invariance on Weakly Compact Subsets

Let  $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are resp...

Relation between Fixed Point and Asymptotical Center of Nonexpansive Maps

Many topics and techniques regarding asymptotic centers and asymptotic radius were studied by Edelstein 1 , Bose and Laskar 2 , Downing and Kirk 3 , Goebel and Kirk 4 , and Lan and Webb 5 . Now, We recall that definitions of asymptotic center and asymptotic radius. Let C be a nonempty subset of a Banach space X and {xn} a bounded sequence in X. Consider the functional ra ·, {xn} : X → R defined by

On Weakly Compact Subsets of Banach Spaces

Introduction. The two sections of this note are independent, but they are related by the fact that both use the results of [5 ] to obtain information on the properties of weakly compact sets in Banach spaces. In the first section we prove some results on a class of compact sets which is believed to include all weakly compact subsets of Banach spaces. We are interested in the properties of the n...

A fixed point theorem for nonexpansive compact self-mapping

A mapping T from a topological space X to a topological space Y is said to be compact if T (X) is contained in a compact subset of Y. The aim of the paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends ...