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

Zeynep Kalkan; Aynur Şahin; Ahmad Aloqaily; Nabil Mlaiki; Zeynep Kalkan; Aynur Şahin; Ahmad Aloqaily; Nabil Mlaiki

doi:10.3934/math.2024556

AIMS Mathematics

2024, Volume 9, Issue 5: 11335-11351. doi: 10.3934/math.2024556

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

1.
Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya, 54050, Turkey
2.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
3.
School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney, 2150, Australia

Received: 26 January 2024 Revised: 06 March 2024 Accepted: 18 March 2024 Published: 22 March 2024
MSC : 47H10, 45B05

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.
- stability,
- fixed point,
- $ b $-metric-like space,
- $ T $-mean nonexpansive mapping,
- Hammerstein integral equation,
- time scale
Citation: Zeynep Kalkan, Aynur Şahin, Ahmad Aloqaily, Nabil Mlaiki. Some fixed point and stability results in $ b $-metric-like spaces with an application to integral equations on time scales[J]. AIMS Mathematics, 2024, 9(5): 11335-11351. doi: 10.3934/math.2024556

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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.

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