Compact asymptotic center and common fixed point in strictly convex Banach spaces

TL;DR

This paper establishes new common fixed point theorems for commuting pairs of generalized nonexpansive mappings in strictly convex Banach spaces, extending existing results in the field.

Contribution

It introduces generalized nonexpansive mappings and proves fixed point theorems that improve upon recent known results in strictly convex Banach spaces.

Findings

Established common fixed point theorems for commuting pairs of mappings.

Extended and improved previous fixed point results.

Applicable to generalized nonexpansive single and multivalued mappings.

Abstract

In this paper, we present some common fixed point theorems for a commuting pair of mappings, including a generalized nonexpansive single valued mapping and a generalized nonexpansive multivalued mapping in strictly convex Banach spaces. The results obtained in this paper extend and improve some recent known results.