Existence and uniqueness of the solution for a general system of operator equations in $b-$metric spaces endowed with a graph

Document Type : Research Paper


Department of Business, Faculty of Business, Babes-Bolyai University, Cluj-Napoca, Romania


The purpose of this paper is to present some coupled fixed point results on a metric space endowed with two $b$-metrics. We shall apply a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces endowed with directed graphs. Data dependence, well-posedness and Ulam-Hyers stability are also studied. The results obtained here will be applied to prove the existence and uniqueness of the solution for a system of integral equations.