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

Abstract

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.