Geodesic
On the Lifshits Constant for Hyperspaces
K. Le/sniak1
1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12//18 87-100 Toru/n, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 2, pp. 155-160

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ba55-2-6
Keywords: lifshits theorem states k uniformly lipschitz map bounded orbit complete metric space has fixed point provided varkappa where varkappa so called lifshits constant many spaces have varkappa interesting whether lifshits theorem theory iterated function systems therefore investigate value lifshits constant several classes hyperspaces

K. Le/sniak 1

1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12//18 87-100 Toru/n, Poland 
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K. Le/sniak. On the Lifshits Constant for Hyperspaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 2, pp. 155-160. doi: 10.4064/ba55-2-6

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