Applications of Multivalued Contractions on Graphs to Graph-Directed Iterated Function Systems

Abstract

We apply a fixed point result for multivalued contractions on complete metric spaces endowed with a graph to graph-directed iterated function systems. More precisely, we construct a suitable metric space endowed with a graph $G$ and a suitable $G$-contraction such that its fixed points permit us to obtain more information on the attractor of a graph-directed iterated function system.