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Research Article | Open Access

A counterexample to the new iterative scheme of Rezapour et al.: Some discussions and corrections

Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
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Abstract

In this paper, we show a counterexample to the new iterative scheme introduced by Rezapour et al. in "A new modified iterative scheme for finding common fixed points in Banach spaces: application in variational inequality problems" [2]. We propose a modified iteration to conclude the convergence result. Moreover, some of our results are established under a weaker assumption.

Keywords

common fixed pointgeneralized α-nonexpansive mappingweak convergencestrong convergenceuniformly convex Banach spacestrictly convex Banach space
CLC number: 47H09, 47H10

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AIMS Mathematics
Volume 8 Issue 4,
April 2023
Pages 9436-9442
DOI: 10.3934/math.2023475

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Saejung S. A counterexample to the new iterative scheme of Rezapour et al.: Some discussions and corrections. AIMS Mathematics, 2023, 8(4): 9436-9442. https://doi.org/10.3934/math.2023475

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Received: 08 January 2023
Revised: 04 February 2023
Accepted: 07 February 2023
Published: 15 April 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)