COMMON FIXED POINT THEOREM IN COMPLETE METRIC SPACE WITH APPLICATION

In this paper, a common fixed point theorem is presented for generalized $\varphi$-weak contraction mappings. Also, we examine the existence and uniqueness of common fixed points for single-valued mappings satisfying the notion of weak compatibility in the setup of complete metric space. Our result generalizes and extends many results existing in literature. An example is given to show that our results are proper generalizations of the existing ones and provide an application to integral equation.