The equivalence among new multistep iteration, s-iteration and some other iterative schemes

TL;DR

This paper demonstrates that various classical and modern iterative schemes are fundamentally equivalent when applied to contractive-like operators, unifying multiple approaches under a common framework.

Contribution

It establishes the equivalence among numerous iterative schemes, including new and existing ones, for contractive-like operators, providing a unified understanding of their behavior.

Findings

All schemes are equivalent for contractive-like operators.

Unifies multiple iterative methods under a common framework.

Simplifies analysis and comparison of iterative schemes.

Abstract

In this paper, we show that Picard, Krasnoselskij, Mann, Ishikawa, new two step, Noor, multistep, new multistep, SP and S-iterative schemes are equivalent for contractive-like operators.