Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A New Iterative Scheme for Approximation of Fixed Points of Suzuki's Generalized Nonexpansive Mappings

Version 1 : Received: 5 May 2021 / Approved: 7 May 2021 / Online: 7 May 2021 (09:05:49 CEST)

How to cite: Rawat, S.; Dimri, R.C.; Bartwal, A. A New Iterative Scheme for Approximation of Fixed Points of Suzuki's Generalized Nonexpansive Mappings. Preprints 2021, 2021050125 (doi: 10.20944/preprints202105.0125.v1). Rawat, S.; Dimri, R.C.; Bartwal, A. A New Iterative Scheme for Approximation of Fixed Points of Suzuki's Generalized Nonexpansive Mappings. Preprints 2021, 2021050125 (doi: 10.20944/preprints202105.0125.v1).

Abstract

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

Subject Areas

Uniformly convex Banach space; Iteration process; Suzuki's generalized nonexpansive mapping; weak convergence; Strong convergence

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