A CONTRACTION PRINCIPLE ON GAUGE SPACES WITH GRAPHS AND APPLICATION TO INFINITE GRAPH -DIRECTED ITERATED FUNCTION SYSTEMS

作者：Dinevari T^*; Frigon M

来源：Fixed Point Theory, 2017, 18(2): 523-544.

DOI：10.24193/fpt-ro.2017.2.41

• Fixed point
• multi-valued map
• contraction
• graph
• graph-directed iterated function system
• infinite system
• attractor gauge space

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.

• 出版日期2017