The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < ϰ(X) where ϰ(X) is the so-called Lifshits constant of X. For many spaces we have ϰ(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-2-6,
author = {K. Le\'sniak},
title = {On the Lifshits Constant for Hyperspaces},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {55},
year = {2007},
pages = {155-160},
zbl = {1124.54002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-2-6}
}
K. Leśniak. On the Lifshits Constant for Hyperspaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 155-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-2-6/