F-Bipolar metric spaces and fixed point theorems with applications

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