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Research Article | Open Access

Some fixed point and stability results in b-metric-like spaces with an application to integral equations on time scales

Zeynep Kalkan1, Aynur Şahin1, Ahmad Aloqaily2,3, Nabil Mlaiki2( )
Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya, 54050, Turkey
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney, 2150, Australia
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Abstract

This paper presents the stability theorem for the T-Picard iteration scheme and establishes the existence and uniqueness theorem for fixed points concerning T-mean nonexpansive mappings within b-metric-like spaces. The outcome of our fixed point theorem substantiated the existence and uniqueness of solutions to the Fredholm-Hammerstein integral equations defined on time scales. Additionally, we provided two numerical examples from distinct time scales to support our findings empirically.

Keywords

stabilityfixed pointb-metric-like spaceT-mean nonexpansive mappingHammerstein integral equationtime scale
CLC number: 47H10, 45B05

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AIMS Mathematics
Volume 9 Issue 5,
May 2024
Pages 11335-11351
DOI: 10.3934/math.2024556

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Cite this article:
Kalkan Z, Şahin A, Aloqaily A, et al. Some fixed point and stability results in b-metric-like spaces with an application to integral equations on time scales. AIMS Mathematics, 2024, 9(5): 11335-11351. https://doi.org/10.3934/math.2024556

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Received: 26 January 2024
Revised: 06 March 2024
Accepted: 18 March 2024
Published: 15 May 2024
©2024 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)