SOME ASPECTS OF INVARIANT MEANS IN THE SPACES OF WEAKLY ALMOST PERIODIC FUNCTIONS AND LEFT UNIFORMLY CONTINUOUS FUNCTIONS

Abstract

The main aim of this paper is to study fixed-point properties for semitopological semigroups ($\mathrm{\Sigma }$) of nonexpansive mappings on a subset of a Banach space which is nonempty, closed and convex or, more generally, a locally convex space, and to establish the fixed-point property of the space of all left uniformly continuous functions by using its amenability for $\mathrm{\Sigma }$ and to establish the fixed-point property for the class of weakly almost periodic functions by using its amenability for $\mathrm{\Sigma }$.