Lipschitz Continuous Selectors, Part I: Linear Selectors

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

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