Common fixed point theorems for (φ,F)-contraction mappings in cone b-metric spaces over Banach algebra with application

Abstract

In this study, the notion of the common fixed point theorem on contraction mappings is established using the class functions. The primary result is a generalization of the common fixed point theorems for (φ,F)-contraction mappings on cone b-metric spaces over Banach algebra A. Investigated are the common fixed points criteria for existence and uniqueness. Suitable examples are provided an illustrate the validity of our results. At the end of this article the existence of common solution for a class of functional equations arising in dynamic programming are demonstrated with the help of our main results.