Title: Convergence results of K iteration process for nonexpansive mappings with an application

Authors: M. Sankara Narayanan; V. Anbukkarasi; M. Marudai

Addresses: Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, 624 302, Tamil Nadu, India ' Department of Mathematics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India ' Department of Mathematics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India

Abstract: This paper deals with the convergence theorems that approximate the fixed points of nonexpansive mappings via K iteration process under the framework of uniformly convex Banach space. One numerical example is provided to illustrate the derived result. Further, based on the proposed result, the existence of the mild solution for wave equation is discussed. In addition to that one new iterative scheme is proposed for finding the fixed points of nonexpansive and quasinonexpansive mappings.

Keywords: K iteration process; uniformly convex Banach space; nonexpansive; quasi-nonexpansive mapping.

DOI: 10.1504/IJDSDE.2021.120042

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.5/6, pp.448 - 461

Received: 19 Apr 2019
Accepted: 30 Aug 2019
Published online: 05 Jan 2022 *

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