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

Abstract

In this paper, we introduce the notions of (F, ϕ, θ)-proximal contraction and (F, ϕ, θ)-weak proximal contraction for non-self mappings and utilize the same to prove some existence and uniqueness of ϕ-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 ϕ-best proximity point, we deduce some best proximity point theorems in the context of partial metric spaces.