Implicit relations related to ordered orbitally complete metric spaces and applications

Abstract

In this study, the notions of asymptotically regular mappings and orbitally continuity are used to prove common fixed point results for four mappings satisfying an implicit relation involving a control function on an ordered orbitally complete metric space. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. We furnish suitable examples to demonstrate the validity of the hypotheses of our results which can fail if some of these condition is missing. It is also verified that the proposed results have an important role to derive applications to certain systems of integral equations. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.