On the Lifshits Constant for Hyperspaces
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 $k<\varkappa(X)$ 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.