'-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.