Common fixed point theorems on orbitally complete ordered metric spaces via asymptotic regularity

In this paper, we prove some common fixed point theorems for a pair of commuting as well as relatively asymptotically regular mappings defined on a (T,R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathcal {T,R})$$\end{document}-orbitally complete metric space employing the orbital continuity of one of the involved maps. We also furnish suitable examples to demonstrate the utility of the hypotheses of our results.