Convex extensions of the convex set valued maps

Guseinov K., Dune S., Ozer O.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.314, no.2, pp.672-688, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 314 Issue: 2
  • Publication Date: 2006
  • Doi Number: 10.1016/j.jmaa.2005.04.019
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.672-688
  • Keywords: set valued map, convex extension, derivative set, Lipschitz continuity, DIFFERENTIAL-INCLUSIONS
  • Anadolu University Affiliated: No

Abstract

In this article the existence of the convex extension of convex set valued map is considered. Conditions are obtained, based on the notion of the derivative of set valued maps, which guarantee the existence of convex extension. The conditions are given, when the convex set valued map has no convex extension. The convex set valued map is specified, which is the maximal convex extension of the given convex set valued map and includes all other convex extensions. The connection between Lipschitz continuity and existence of convex extension of the given convex set valued map is studied. (c) 2005 Elsevier Inc. All rights reserved.