Bregman nonexpansive type actions of semitopological semigroups

TL;DR

This paper investigates fixed point existence for Bregman nonexpansive type actions of semitopological semigroups on convex subsets of reflexive Banach spaces, under certain amenability conditions.

Contribution

It extends fixed point theory to Bregman nonexpansive actions of semitopological semigroups, including hybrid, nonspreading, and asymptotically nonexpansive mappings.

Findings

Established fixed point existence under amenability conditions

Included various Bregman nonexpansive mapping classes

Provided new fixed point results for semigroup actions

Abstract

Let $S$ be a semitopological semigroup, and let $C$ be a nonempty closed convex subset of a reflexive Banach space. Under some amenability conditions on $S$, we provide existence results of fixed points for several Bregman nonexpansive type actions $S\times C\to C$, $(s,x)\mapsto T_s x$, of $S$ on $C$. The mappings $T_s$ we discuss include those being Bregman generalized hybrid, Bregman nonspreading, and Bregman left asymptotically nonexpansive.