SET-VALUED G-PRESIC TYPE F-CONTRACTIONS AND FIXED POINT THEOREMS

The aim of this paper is to define set-valued G-Presic type F-contraction on product spaces when the underlying space is a complete metric space endowed with a graph. Some fixed point theorems for the so-called set-valued G-Presic type F-contraction are established. Our results 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.