Weak and strong convergence of an implicit iterative process with errors for a finite family of asymptotically quasi $I-$nonexpansive mappings in Banach space

TL;DR

This paper establishes the weak and strong convergence of an implicit iterative process with errors to common fixed points for families of asymptotically quasi nonexpansive mappings in Banach spaces.

Contribution

It proves convergence results for an implicit iterative process involving errors for a finite family of asymptotically quasi nonexpansive mappings in Banach spaces, extending existing fixed point theory.

Findings

Proves weak convergence of the iterative process.

Establishes strong convergence under certain conditions.

Handles errors in the iterative process.

Abstract

In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family $\{T_j\}_{i=1}^N$ of asymptotically quasi $I_j-$nonexpansive mappings as well as a family of $\{I_j\}_{j=1}^N$ of asymptotically quasi nonexpansive mappings in the framework of Banach spaces.