Strong convergence of modified Ishikawa iterations for nonlinear mappings

TL;DR

This paper establishes a strong convergence theorem for modified Ishikawa iterations applied to a class of nonlinear mappings in Banach spaces, extending previous results in the field.

Contribution

It introduces a new convergence theorem for modified Ishikawa iterations for relatively asymptotically nonexpansive mappings, improving upon recent existing results.

Findings

Proves strong convergence of the iterative method

Extends applicability to broader class of mappings

Improves convergence conditions compared to prior work

Abstract

In this paper, we prove a strong convergence theorem of modified Ishikawa iterations for relatively asymptotically nonexpansive mappings in Banach space. Our results extend and improve the recent results by Nakajo, Takahashi, Kim, Xu, Matsushita and some others.