F-Bipolar metric spaces and fixed point theorems with applications

Abstract

In this paper, we propose a new generalization of metric spaces by the unification of two novel notions, namely \(\mathfrak{F}\)-metric spaces and bipolar metric spaces, under the name \(\mathfrak{F}\)-bipolar metric spaces. Further, in this newly generalized notion we provide a binary topology and prove some fixed point results. As applications of our result, we prove the existence and uniqueness of solution of integral equation and the existence of a unique solution in homotopy theory. We also give some non-trivial examples to vindicate our claims. Our fixed point results extend several results in the existing literature.