Infinite Iterated Function Systems: A Multivalued Approach

K. Leśniak. "Infinite Iterated Function Systems: A Multivalued Approach." Bulletin of the Polish Academy of Sciences. Mathematics 52.1 (2004): 1-8. <http://eudml.org/doc/280281>.

@article{K2004,
abstract = {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.},
author = {K. Leśniak},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Hausdorff measure of noncompactness; condensing multifunction; iterated function system; uniformly Hausdorff upper semicontinuous multifunction},
language = {eng},
number = {1},
pages = {1-8},
title = {Infinite Iterated Function Systems: A Multivalued Approach},
url = {http://eudml.org/doc/280281},
volume = {52},
year = {2004},
}

TY - JOUR
AU - K. Leśniak
TI - Infinite Iterated Function Systems: A Multivalued Approach
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 1
SP - 1
EP - 8
AB - 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.
LA - eng
KW - Hausdorff measure of noncompactness; condensing multifunction; iterated function system; uniformly Hausdorff upper semicontinuous multifunction
UR - http://eudml.org/doc/280281
ER -