
Journal of Convex Analysis 18 (2011), No. 3, 737747 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, 00661 Warsaw, Poland Tadeusz Rzezuchowski Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00661 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 [ Fulltextpdf (128 KB)] for subscribers only. 