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Journal of Convex Analysis, Vol. 5, No. 2, pp. 249-267 (1998)
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Lipschitz Continuous Selectors, Part I: Linear Selectors

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Krzysztof Przeslawski

Instytut Matematyki, Politechnika Zielonogorska, ul. Podgorna 50, 65-246 Zielona Gora, Poland, K.Przeslawski@im.pz.zgora.pl

**Abstract:** We study various properties of Lipschitz continuous linear selectors on the family of all convex, nonempty and compact subsets of $\mathbb{R}^n$. In particular, it is shown that if $s$ is such a selector then the Lipschitz constant of $s$ can be estimated from below by the norm of $s(B^n)$, where $B^n$ is the unit ball. A notion of a parametric representation of convex bodies is introduced and illustrated with examples.

**Classification (MSC2000):** 54C65, 54C60, 52Axx

**Full text of the article:**

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