In this paper, we employ two types of implicit relations to define some new kind proximal contractions and study about their best proximity points. More precisely, use class functions $\mathcal{A}$ $\mathcal{A}'$ explore $\mathcal{A}$, $\mathcal{A}'$-contractions first second type strong $\mathcal{A}'$-contractions. We investigate the existence point results same. It is worth mentioning that we...

In this paper, we introduce a pair of generalized proximal contraction mappings and prove the existence of a unique best proximity point for such mappings in a complete metric space. We provide examples to illustrate our result. Our result extends some of the results in the literature.

Abstract The aim of this article is to introduce α \alpha - ψ \psi -proximal contraction in the setting ℱ -metric space and prove existence best proximity points for these contractions. As applications our main results, we obtain coupled on equipped with an arbitrary binary relation.