A contraction principle on gauge spaces with graphs and application to infinite graph-directed iterated function systems


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	A contraction principle on gauge spaces with graphs and application to infinite graph-directed iterated function systems


	Fixed Point Theory, Volume 18, No. 2, 2017, 523-544, June 1st, 2017 DOI: 10.24193/fpt-ro.2017.2.41 Authors: T. Dinevari and M. Frigon Abstract: We consider multi-valued maps defined on a complete gauge space endowed with a directed graph. We establish a fixed point result for maps which send connected points into connected points and satisfy a generalized contraction condition. Then, we study infinite graph-directed iterated function systems (H-IIFS).We give conditions insuring the existence of a unique attractor to an H-IIFS. Finally, we apply our fixed point result for multi-valued contractions on gauge spaces endowed with a graph to obtain more information on the attractor of an H-IIFS. More precisely, we construct a suitable gauge space endowed with a graph G and a suitable multi-valued G-contraction such that its fixed points are sub-attractors of the H-IIFS. Key Words and Phrases: Fixed point, multi-valued map, contraction, graph, graph-directed iterated function system, infinite system, attractor gauge space. 2010 Mathematics Subject Classification: 47H10, 47H04, 47H09, 28A80, 54E15. Published on-line: June 1st, 2017. Abstract pdf Fulltext pdf Back to volume's table of contents