Estimation of Newly Established Iterative Scheme for Generalized Nonexpansive Mappings

Aftab Hussain,Nawab Hussain,Danish Ali,Maria Alessandra Ragusa

doi:10.1155/2021/6675979

Abstract

We introduce a new iterative method in this article, called the D iterative approach for fixed point approximation. Analytically, and also numerically, we demonstrate that our established D I.P is faster than the well-known I.P of the prior art. Finally, in a uniformly convex Banach space environment, we present weak as well as strong convergence theorems for Suzuki’s generalized nonexpansive maps. Our findings are an extension, refinement, and induction of several existing iterative literatures.

Highlights

Introduction and PreliminariesIn many branches of mathematics and various sciences, the existence of a fixed point is crucial
In [2], the writer believes that the approximation rate of the Agarwal I.P is like that of the Picard I.P and is faster than the contraction mapping of the Mann I.P
In [9], the writers help by numerical examples to prove for nonexpansive mapping, that the approximation rate of the Picard-S I.P is better than existing literature

Summary

Introduction

Introduction and PreliminariesIn many branches of mathematics and various sciences, the existence of a fixed point is crucial. The approximation rate for the latest I.P is contrasted with the Agarwal I.P, Picard-S I.P, M I.P, M∗ I.P, and K I.P. We present the weak as well as strong convergence theorems of Suzuki generalized nonexpansive maps and contraction map for our newly developed I.P. We first remember those definitions, ideas, and lemmas which we have to use in the upcoming two sections. The fixed point theorem of the Suzuki generalized nonexpansive mapping has been studied by many authors [5,6,7].

Results

Conclusion