A fixed point theorem for monotone asyptotic nonexpansive mappings

TL;DR

This paper extends fixed point theory to monotone asymptotic nonexpansive mappings in Banach spaces, establishing conditions for the existence of fixed points similar to classical theorems.

Contribution

It introduces a new fixed point theorem for monotone asymptotic nonexpansive mappings, generalizing previous results in the field.

Findings

Established a fixed point existence theorem for the class of mappings

Extended classical fixed point results to asymptotic nonexpansive mappings

Provided conditions under which fixed points exist for these mappings

Abstract

Let C be a nonempty, bounded, closed, and convex subset of a Banach space X and $T : C \rightarrow C$ be a monotone asymptotic nonexpansive mapping. In this paper, we investigate the existence of fixed points of T. In particular, we establish an analogue to the original Goebel and Kirk's fixed point theorem for asymptotic nonexpansive mappings.