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A+ CATEGORY SCIENTIFIC UNIT

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

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.

Authors

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

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