Best proximity point theorems for generalized α-β-proximal quasi-contractive mappings

Abstract

Abstract Herein, we search for some best proximity point results for a novel class of non-self-mappings T : A ⟶ B $T:A \longrightarrow B$ called generalized proximal α-β-quasi-contractive. We illustrate our work by an example. Our results generalize and extend many recent results appearing in the literature. Several consequences are derived. As applications, we explore the existence of best proximity points for a metric space endowed with symmetric binary relation.

Keywords

• best proximity points
• α-β-proximal quasi-contractive mappings on metric spaces