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...

best approximation results provide an approximate solution to the fixed point equation $tx=x$, when the non-self mapping $t$ has no fixed point. in particular, a well-known best approximation theorem, due to fan cite{5}, asserts that if $k$ is a nonempty compact convex subset of a hausdorff locally convex topological vector space $e$ and $t:krightarrow e$ is a continuous mapping, then there exi...

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.

Fixed point theory and contractive mappings are popular tools in solving a variety of problems such as control theory, economic nonlinear analysis global analysis.There many works on different types contractions to find fixed metric spaces. Improving extending some kind those, this paper, we introduce new version H-contradiction for four space (X,d). Then, prove the existence uniqueness common ...