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Regularity of set-valued maps and their selections through set differences. Part 2: One-sided Lipschitz properties

URN zum Zitieren dieses Dokuments: urn:nbn:de:bvb:703-epub-1904-3

Titelangaben

Baier, Robert ; Farkhi, Elza:
Regularity of set-valued maps and their selections through set differences. Part 2: One-sided Lipschitz properties.
Department of Mathematics, University of Bayreuth
Bayreuth, Germany , 2013 . - 29 S.

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Angaben zu Projekten

Projekttitel:
Offizieller ProjekttitelProjekt-ID
Hermann Minkowski Center for GeometryOhne Angabe
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)264735-SADCO

Projektfinanzierung: Andere
Hermann Minkowski Center for Geometry at Tel-Aviv University, Israel; European Union "FP7-People-ITN" programme

Abstract

We introduce one-sided Lipschitz (OSL) conditions of set-valued maps with respect to given set differences. The existence of selections of such maps that pass through any point of their graphs and inherit uniformly their OSL constants is studied. We show that the OSL property of a convex-valued set-valued map with respect to the Demyanov difference with a given constant is characterized by the same property of the generalized Steiner selections. We prove that an univariate OSL map with compact images in IR^1 has OSL selections with the same OSL constant. For such a multifunction which is OSL with respect to the metric difference, one-sided Lipschitz metric selections exist through every point of its graph with the same OSL constant.

Weitere Angaben

Publikationsform: Preprint, Postprint, Working paper, Diskussionspapier
Zusätzliche Informationen (öffentlich sichtbar): Special issue dedicated to the 65th anniversary of Professor Asen L. Dontchev and to the 60th anniversary of Professor Vladimir M. Veliov.
Contents:
1. Introduction
2. Set differences and their properties
3. OSL multimaps through set differences
3.1 One-sided Lipschitz conditions
3.2 Properties and relations between the different notions
4. One-sided Lipschitz selections
4.1 One-sided Lipschitz conditions
4.2 One-sided Lipschitz metric selections
4.3 One-sided Lipschitz selections of OSL maps
5. Examples
5.1 Examples illustrating strict inclusions in Theorem 3.17
5.2 Examples for Lipschitz selections
Conclusions
Keywords: one-sided Lipschitzian set-valued maps; selections; generalized Steiner selection; metric selection; set differences; Demyanov difference; metric difference
Fachklassifikationen: Mathematics Subject Classification Code: 47H06 (54C65 47H04 54C60 26E25)
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Institutionen der Universität: Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Profilfelder
Profilfelder > Advanced Fields
Profilfelder > Advanced Fields > Nichtlineare Dynamik
Sprache: Englisch
Titel an der UBT entstanden: Ja
URN: urn:nbn:de:bvb:703-epub-1904-3
Eingestellt am: 09 Mrz 2015 11:49
Letzte Änderung: 11 Mrz 2015 09:57
URI: https://epub.uni-bayreuth.de/id/eprint/1904