Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Andrzej Leśniewski

Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

Tadeusz Rzeżuchowski

Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

T.Rzezuchowski@mini.pw.edu.pl

Keywords

  • Convex and bounded sets
  • Demyanov metric
  • Hausdorff metric
  • linear selectors

Mathematics Subject Classification

52A20, 54C65, 58C06, 54E35

Suggested citation

A. Leśniewski, T. Rzeżuchowski. “The Demyanov Metric for Convex, Bounded Sets and Existence of Lipschitzian Selectors.” Journal of Convex Analysis 18 (2011), No. 3, 737–747. https://doi.org/10.68381/jca18047

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press.