Set-valued contractions with an application to Fredholm integral inclusions in $ {m_v^b}- $metric spaces

Khairul Habib Alam; Yumnam Rohen; Anita Tomar; Mohammad Sajid; Khairul Habib Alam; Yumnam Rohen; Anita Tomar; Mohammad Sajid

doi:10.3934/math.2025926

AIMS Mathematics

2025, Volume 10, Issue 9: 20742-20758. doi: 10.3934/math.2025926

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Set-valued contractions with an application to Fredholm integral inclusions in $ {m_v^b}- $metric spaces

1.
Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal, 795004, Manipur, India
2.
Department of Mathematical Sciences, Indian Institute of Science Education and Research Berhampur, Laudigam, Berhampur, 760003, Odisha, India
3.
Department of Mathematics, Manipur University, Canchipur, Imphal, 795003, Manipur, India
4.
Pt. L. M. S. Campus, Sridev Suman Uttarakhand University, Ganga Nagar, Rishikesh, 246201, Uttarakhand, India
5.
Department of Mechanical Engineering, College of Engineering, Qassim University, Saudi Arabia

Received: 05 August 2025 Revised: 31 August 2025 Accepted: 03 September 2025 Published: 09 September 2025
MSC : 47H10, 52H25, 54B20, 54E50

This study investigates set-valued contractions within the framework of $ {m_v^b-} $metric spaces, extending classical contraction principles. By introducing and examining the Hausdorff $ {m_v^b-} $metric, we establish a foundation for set-valued fixed point theorems, thereby contributing significantly to this area of research. Our findings generalize several well-known contraction concepts, including those of Banach, Sehgal, Wardowski, Altun, Bianchini, and Nadler, within the context of $ {m_v^b-} $metric spaces. These advancements have practical implications, particularly in the study of nonlinear systems and the mathematical model of Fredholm integral inclusions. The results presented here emphasize the growing importance of set-valued fixed points and pave the way for further exploration and application across various scientific and engineering domains.
- $ F- $contraction,
- Hausdorff $ {m_v^b}- $metric,
- Sehgal contraction,
- nonlinear systems,
- mathematical model of Fredholm integral inclusion
Citation: Khairul Habib Alam, Yumnam Rohen, Anita Tomar, Mohammad Sajid. Set-valued contractions with an application to Fredholm integral inclusions in $ {m_v^b}- $metric spaces[J]. AIMS Mathematics, 2025, 10(9): 20742-20758. doi: 10.3934/math.2025926

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Abstract

This study investigates set-valued contractions within the framework of $ {m_v^b-} $metric spaces, extending classical contraction principles. By introducing and examining the Hausdorff $ {m_v^b-} $metric, we establish a foundation for set-valued fixed point theorems, thereby contributing significantly to this area of research. Our findings generalize several well-known contraction concepts, including those of Banach, Sehgal, Wardowski, Altun, Bianchini, and Nadler, within the context of $ {m_v^b-} $metric spaces. These advancements have practical implications, particularly in the study of nonlinear systems and the mathematical model of Fredholm integral inclusions. The results presented here emphasize the growing importance of set-valued fixed points and pave the way for further exploration and application across various scientific and engineering domains.

References

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