New type of $\alpha − F−$ contraction on common fixed point theorems in metric spaces and its application

Abstract

In this paper we introduce the notion of  $F−$  contraction via  $\alpha−$  admissible pair of mappings. We also provide many common fixed point results regarding rational expressions in the setting of metric spaces. Moreover, we also present some illustrated examples as an application of this concept and we also establish an existence theorem for integral equations.