The Existence of Best Proximity Points of Generalized $p$-Cyclic Weak $(F,\psi,\varphi)$ Contractions in $p$-Cyclic Metric Spaces

Abstract

In this manuscript, we discuss some property of $p$-cyclic maps which belong to the class $\Omega$  and we extend the notion of a generalized cyclic weak $(F,\psi ,\varphi )$-contractin to a generalized $p$-cyclic weak $(F,\psi ,\varphi )$-contraction, where $p \ge 2$. We prove best proximity point results of such map in $p$-cyclic complete metric spaces. Our results extend and generalize the related result in the literature. We also give an example in support of our main result.