Some convergence results in modular spaces with application to a system of integral equations

Abdurrahman Büyükkaya; Mudasir Younis; Dilek Kesik; Mahpeyker Öztürk; Abdurrahman Büyükkaya; Mudasir Younis; Dilek Kesik; Mahpeyker Öztürk

doi:10.3934/math.20241497

AIMS Mathematics

2024, Volume 9, Issue 11: 31030-31056. doi: 10.3934/math.20241497

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Some convergence results in modular spaces with application to a system of integral equations

1.
Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey
2.
Department of Mathematics, Sakarya University, 54050, Sakarya, Turkey

Received: 20 August 2024 Revised: 17 October 2024 Accepted: 21 October 2024 Published: 31 October 2024
MSC : 47H10, 45B05, 54H25

The paper aimed to achieve three primary objectives. First, it introduced significant common fixed point results in the context of newly proposed partial modular $ b- $metric spaces, thus contributing to the advancement of this field. Second, it presented unique results using a direct approach that did not depend on the strong continuity of the mapping, thereby offering a valuable perspective. Finally, it applied previously established convergence techniques to determine a common solution for a system of Fredholm integral equations, demonstrating the practical implications of the theoretical findings.
- fixed point,
- partial modular $ b- $metric,
- Proinov type contraction,
- Fredholm integral equation
Citation: Abdurrahman Büyükkaya, Mudasir Younis, Dilek Kesik, Mahpeyker Öztürk. Some convergence results in modular spaces with application to a system of integral equations[J]. AIMS Mathematics, 2024, 9(11): 31030-31056. doi: 10.3934/math.20241497

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Abstract

The paper aimed to achieve three primary objectives. First, it introduced significant common fixed point results in the context of newly proposed partial modular $ b- $metric spaces, thus contributing to the advancement of this field. Second, it presented unique results using a direct approach that did not depend on the strong continuity of the mapping, thereby offering a valuable perspective. Finally, it applied previously established convergence techniques to determine a common solution for a system of Fredholm integral equations, demonstrating the practical implications of the theoretical findings.

References

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