?-Best proximity point theorems in metric spaces with applications in partial metric spaces

Abstract

In this paper, we introduce the notions of (F, ?, ?)-proximal contraction and (F, ?, ?)-weak proximal contraction for non-self mappings and utilize the same to prove some existence and uniqueness of ?-best proximity point for such mappings. Some illustrative examples are also given to exhibit the utility of our results. As an application of the concept of ?-best proximity point, we deduce some best proximity point theorems in the context of partial metric spaces.