On some strong convergence results of a new Halpern-type iterative process for quasi-nonexpansive mappings and accretive operators in Banach spaces

TL;DR

This paper introduces a new iterative process in Banach spaces that strongly converges to common fixed points of quasi-nonexpansive mappings and zeros of accretive operators, improving existing results.

Contribution

The paper presents a novel iterative process that guarantees strong convergence for both fixed points and zeros of operators in Banach spaces, extending previous methods.

Findings

Converges strongly to common fixed points of quasi-nonexpansive mappings.

Achieves strong convergence to zeros of accretive operators.

Generalizes many existing convergence results.

Abstract

In this study, we introduce a new iterative processes to approximate common fixed points of an infinite family of quasi-nonexpansive mappings and obtain a strongly convergent iterative sequence to the common fixed points of these mappings in a uniformly convex Banach space. Also we prove that this process to approximate zeros of an infinite family of accretive operators and we obtain a strong convergence result for these operators. Our results improve and generalize many known results in the current literature.