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Research Article | Open Access

Further generalizations of the Ishikawa algorithm

Mohammad Reza Haddadi1( ), Vahid Parvaneh2, Monica Bota3( )
Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran
Department of Mathematics, Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania
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Abstract

We provide an iterative algorithm for fixed point issues in vector spaces in the paragraphs that follow. We demonstrate that, compared to the Ishikawa technique in Banach spaces, the iterative algorithm presented in this study performs better under weaker conditions. In order to achieve this, we compare the convergence behavior of iterations, and taking into account a few offered cases, we support the major findings.

Keywords

best proximity pointfixed pointuniformly convex Banach spaceiterative sequence
CLC number: 90C48, 47H09, 46B20

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AIMS Mathematics
Volume 8 Issue 5,
May 2023
Pages 12185-12194
DOI: 10.3934/math.2023614

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Cite this article:
Haddadi MR, Parvaneh V, Bota M. Further generalizations of the Ishikawa algorithm. AIMS Mathematics, 2023, 8(5): 12185-12194. https://doi.org/10.3934/math.2023614

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Received: 27 October 2022
Revised: 06 March 2023
Accepted: 08 March 2023
Published: 15 May 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)