Some Convergence And Stability Results For The Kirk Multistep And Kirk-Sp Fixed Point Iterative Algorithms For Contractive-Like Operators In Normed Linear Spaces

TL;DR

This paper introduces a new Kirk multistep iterative algorithm for contractive-like operators in normed spaces, analyzing its convergence and stability, and generalizing existing results in the literature.

Contribution

It proposes a novel Kirk multistep iteration method and establishes convergence and stability theorems, extending previous work on iterative algorithms for contractive operators.

Findings

The Kirk multistep iteration converges under certain conditions.

Stability results are established for Kirk-multistep and Kirk-SP iterations.

The results unify and extend existing convergence theorems.

Abstract

The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related with the stability results for the Kirk-multistep and Kirk-SP iterative processes by employing certain contractive-like operators. Our results generalize and unify some other results in the literature.