On monotone Ćirić quasi-contraction mappings with a graph

Abstract

In this paper, we obtain sufficient conditions for the existence of fixed points for monotone quasi-contraction mappings in metric and modular metric spaces endowed with a graph. This is the extension of Ran and Reurings and Jachymski fixed point theorems for monotone contraction mappings in partially ordered metric spaces and in metric spaces endowed with a graph to the case of quasi-contraction mappings introduced by Ćirić.