Journal of Convex Analysis 18 (2011), No. 3, 737--747
Copyright Heldermann Verlag 2011
The Demyanov Metric for Convex, Bounded Sets and Existence of Lipschitzian Selectors
Andrzej Lesniewski
Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
Tadeusz Rzezuchowski
Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
T.Rzezuchowski@mini.pw.edu.pl
It is shown that an alternative formula for the Demyanov metric permits to extend this metric to the family of convex, bounded sets which need not be closed. Existence of Lipschitzian, linear selectors is discussed.
Keywords: Convex and bounded sets, Demyanov metric, Hausdorff metric, linear selectors.
MSC: 52A20, 54C65, 58C06, 54E35
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