A best proximity point theorem for α-proximal Geraghty non-self mappings

Abstract

Abstract In this paper, we search some best proximity point results for a new class of non-self mappings T:A⟶B $T:A \longrightarrow B$ called α-proximal Geraghty mappings. Our results extend many recent results appearing in the literature. We suggest an example to support our result. Several consequences are derived. As applications, we investigate the existence of best proximity points for a metric space endowed with symmetric binary relation.

Keywords

• Best proximity points
• α-Proximal Geraghty non-self mappings on metric spaces