On the Lifshits Constant for Hyperspaces
Volume 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 155-160
MSC: 54B20, 51K99, 46B20
DOI: 10.4064/ba55-2-6
Abstract
The Lifshits theorem states that any -uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k<\varkappa(X) where \varkappa(X) is the so-called Lifshits constant of X. For many spaces we have \varkappa(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.