Set-valued mappings and best proximity points: A study in $ \mathcal{F} $-metric spaces

Amer Hassan Albargi; Amer Hassan Albargi

doi:10.3934/math.20241612

AIMS Mathematics

2024, Volume 9, Issue 12: 33800-33817. doi: 10.3934/math.20241612

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Research article

Set-valued mappings and best proximity points: A study in $ \mathcal{F} $-metric spaces

Amer Hassan Albargi ^,

Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 02 September 2024 Revised: 31 October 2024 Accepted: 12 November 2024 Published: 28 November 2024
MSC : 46S40, 47H10, 54H25

This paper introduces the concept of set-valued almost $ \Upsilon $-contractions in $ \mathcal{F} $-metric spaces, aiming to obtain the best proximity point results for set-valued mappings. The newly proposed idea of set-valued almost $ \Upsilon $-contractions includes various contractive conditions like set-valued almost contractions, set-valued $ \Upsilon $-contractions, and traditional $ \Upsilon $-contractions. Consequently, the results presented here extend and unify numerous established works in this domain. To illustrate the practical significance of the theoretical findings, a specific example is provided.
- best proximity points,
- set-valued almost $ \Upsilon $-contractions,
- $ \mathcal{F} $-metric spaces,
- fixed points
Citation: Amer Hassan Albargi. Set-valued mappings and best proximity points: A study in $ \mathcal{F} $-metric spaces[J]. AIMS Mathematics, 2024, 9(12): 33800-33817. doi: 10.3934/math.20241612

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Abstract

This paper introduces the concept of set-valued almost $ \Upsilon $-contractions in $ \mathcal{F} $-metric spaces, aiming to obtain the best proximity point results for set-valued mappings. The newly proposed idea of set-valued almost $ \Upsilon $-contractions includes various contractive conditions like set-valued almost contractions, set-valued $ \Upsilon $-contractions, and traditional $ \Upsilon $-contractions. Consequently, the results presented here extend and unify numerous established works in this domain. To illustrate the practical significance of the theoretical findings, a specific example is provided.

References

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