On interpolative F-contractions with shrink map

Abstract

In this article, we introduce two notions of interpolative F-contractions with shrink map and F-contractions with shrink map. We also study the existence of E-fixed points by using these notations on a metric space endowed with a binary relation. As an application and consequence of the main results, we also get some other interesting results like a common fixed point result, an E-fixed point result on a metric space equipped with graph, and an existence theorem for a solution of integral equations.