Common Fixed Point Theorems for Asymptotically Regular Mappings on Ordered Orbitally Complete Metric Spaces with an Application to Systems of Integral Equations

In this paper, we prove existence and uniqueness results for common fixed points of two or three relatively asymptotically regular mappings satisfying the orbital continuity of one of the involved maps on ordered orbitally complete metric spaces under generalized Phi-contractive condition. Also, we introduce and use orbitally dominating maps and orbitally weakly increasing maps. We furnish suitable examples to demonstrate the usability of the hypotheses of our results. As an application, we prove the existence of solutions for certain system of integral equations.