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

Shivam Rawat; Ramesh Chandra Dimri; Ayush Bartwal

doi:10.20944/preprints202105.0125.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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.

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

MATHEMATICS & COMPUTER SCIENCE, General Mathematics

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

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