Common Fixed Point Theorem for Hybrid Pair of Mappings in a Generalized $(F,\xi,\eta)$-contraction in weak Partial $b$- Metric Spaces with an Application

Abstract

In the present paper, we proved a common fixed-point theorem for two-hybrid pair of non-self mappings satisfying a generalized $(F, \xi, \eta) $- contraction condition under joint common limit range property in weak partial $b$- metric spaces. Our result is a generalization of many works available in metric space setting. An example and application to the integral equation are given to support the results proved in this paper.