On the Lifshits Constant for Hyperspaces

Volume 55 / 2007

K. Le/sniak Bulletin Polish Acad. Sci. Math. 55 (2007), 155-160 MSC: 54B20, 51K99, 46B20 DOI: 10.4064/ba55-2-6


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.


  • K. Le/sniakFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12//18
    87-100 Toru/n, Poland

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