Abstract
In this paper, we consider the set-valued contractions defined on product spaces when the underlying space is a complete metric space endowed with a graph. Some fixed point results for the so-called set-valued G-Presic operators are established. Our theorems extend and generalize some known results in product spaces of the recent literature. As an application of our main result, fixed point results for various types of set-valued contractions on product spaces are derived, and a sufficient condition for the existence of a weakly asymptotically stable and global attractor equilibrium point of a kth order nonlinear difference inclusion is established.