Fixed points of the Barnsley-Hutchinson operators induced by hyper-condensing maps

  • Krzysztof Leśniak
Keywords: Hyper-condensing map, Condensing map, Barnsley-Hutchinson operator, Maximal fixed point, Global attractor, Hausdorff measure of noncompactness, Hyperspace, Space of multifunctions


The aim of this note is to show that the Barnsley-Hutchinson operator, induced by either single h-bounded hyper-condensing map or a compact infinite family of such maps, admits a maximal fixed point and global attractor.
Under suitable continuity conditions both fixed point and attractor coincide.
This improves and extends several earlier results.
To obtain these results some new properties of the Hausdorff measure of noncompactness on the hyperspace are established.