Convergence of modified Picard-Mann hybrid iteration process for nearly nonexpansive mappings

TL;DR

This paper establishes strong convergence theorems for nearly nonexpansive mappings using a modified Picard-Mann hybrid iteration in uniformly convex Banach spaces, advancing iterative methods in nonlinear analysis.

Contribution

It introduces a new convergence theorem for nearly nonexpansive mappings with a modified iterative process in Banach spaces.

Findings

Proved strong convergence theorems for nearly nonexpansive mappings.

Validated the effectiveness of the modified Picard-Mann hybrid iteration.

Extended convergence results to uniformly convex Banach spaces.

Abstract

In this paper, we prove the strong convergence theorems for nearly nonexpansive mappings, using the modified Picard-Mann hybrid iteration process in the context of uniformly convex Banach space.