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

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.

Keywords

• best proximity points
• set-valued almost $ \upsilon $-contractions
• $ \mathcal{f} $-metric spaces
• fixed points