Fixed Point Approximation of Suzuki Generalized Nonexpansive Mappings via New Faster Iteration Process

TL;DR

This paper introduces a new, faster iteration method called the K iteration process for fixed point approximation, demonstrating improved convergence speed over existing methods in Banach spaces.

Contribution

The paper proposes the K iteration process, establishing its superiority in speed and stability for fixed point approximation of Suzuki generalized nonexpansive mappings.

Findings

K iteration process converges faster than existing methods

Proved stability and data dependence results for contraction mappings

Established weak and strong convergence theorems in Banach spaces

Abstract

In this paper we propose a new iteration process, called the K iteration process, for approximation of fixed points. We show that our iteration process is faster than the existing leading iteration processes like Picard-S iteration process, Thakur New iteration process and Vatan Twostep iteration process for contraction mappings. We support our analytic proof by a numerical example. Stability of K iteration process and data dependence result for contraction mappings by employing K iteration process is also discussed. Finally we prove some weak and strong convergence theorems for the Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach space. Our results are extension, improvement and generalization of many known results in the literature of fixed point theory.