Approximating fixed points of asymptotically nonexpansive mappings in Banach spaces by metric projections

TL;DR

This paper establishes a strong convergence theorem for asymptotically nonexpansive mappings in uniformly convex and smooth Banach spaces, extending previous results for nonexpansive mappings using metric projections.

Contribution

It introduces a new strong convergence theorem for asymptotically nonexpansive mappings in Banach spaces, improving upon prior theorems for nonexpansive mappings.

Findings

Proves a strong convergence theorem using metric projections.

Extends previous results from nonexpansive to asymptotically nonexpansive mappings.

Applicable in uniformly convex and smooth Banach spaces.

Abstract

In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence theorem due to Matsushita and Takahashi [ Appl. Math. Comput. 196 (2008) 422-425] which was established for nonexpansive mappings.