Best proximity points for generalized (F, R)-proximal contractions

Abstract

We present the notion of generalized (F, R)-proximal non-self contractions and prove best proximity point theorems in complete metric spaces endowed with an arbitrary binary relation. An example is given to vindicate our claims. We also show that the edge preserving structure is a particular case of the binary relation R. Moreover, an application to variational inequality problem is given in order to demonstrate the efficacy of our results.