Convex extensions of the convex set valued maps

Guseinov K., Dune S., Ozer O.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.314, sa.2, ss.672-688, 2006 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 314 Sayı: 2
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.jmaa.2005.04.019
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.672-688
  • Anahtar Kelimeler: set valued map, convex extension, derivative set, Lipschitz continuity, DIFFERENTIAL-INCLUSIONS
  • Anadolu Üniversitesi Adresli: Hayır

Özet

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.