Displaying similar documents to “Stability and invariance of multivalued iterated function systems”

Invariant sets and Knaster-Tarski principle

Krzysztof Leśniak (2012)

Open Mathematics

Similarity:

Our aim is to point out the applicability of the Knaster-Tarski fixed point principle to the problem of existence of invariant sets in discrete-time (multivalued) semi-dynamical systems, especially iterated function systems.

Infinite Iterated Function Systems: A Multivalued Approach

K. Leśniak (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We prove that a compact family of bounded condensing multifunctions has bounded condensing set-theoretic union. Compactness is understood in the sense of the Chebyshev uniform semimetric induced by the Hausdorff distance and condensity is taken w.r.t. the Hausdorff measure of noncompactness. As a tool, we present an estimate for the measure of an infinite union. Then we apply our result to infinite iterated function systems.