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On the Lifshits constant for hyperspaces

Leśniak K.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 2

155-160

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 < x(X] where x(X) is the so-called Lifshits constant of X. For many spaces we have x(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.