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Abstract and Applied Analysis
Volume 2015, Article ID 345856, 16 pages
Research Article

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

Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, QC, Canada H3C 3J7

Received 12 August 2014; Accepted 18 December 2014

Academic Editor: Naseer Shahzad

Copyright © 2015 T. Dinevari and M. Frigon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 and a suitable -contraction such that its fixed points permit us to obtain more information on the attractor of a graph-directed iterated function system.