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Baier, Robert ; Farkhi, Elza:
Regularity of set-valued maps and their selections through set differences. Part 2: One-sided Lipschitz properties.
In: Serdica Mathematical Journal.
Bd. 39
(2013)
Heft 3-4
.
- S. 391-422.
ISSN 1310-6600
| Rez.: |
Dies ist die aktuelle Version des Eintrags.
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Offizieller Projekttitel Projekt-ID Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO) 264735-SADCO Hermann Minkowski Center for Geometry at Tel-Aviv University, Israel Ohne Angabe |
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| Projektfinanzierung: |
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union Andere |
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 ℝ¹ [$\R^1$] 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.
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| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Zusätzliche Informationen: | 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 OSL generalized Steiner selections 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 of one-sided 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) |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) Profilfelder > Advanced Fields > Nichtlineare Dynamik Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut Profilfelder Profilfelder > Advanced Fields |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 19 Mär 2015 08:45 |
| Letzte Änderung: | 02 Jun 2021 10:02 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/8515 |
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Regularity of set-valued maps and their selections through set differences. Part 2: One-sided Lipschitz properties. (deposited 14 Mär 2015 22:00)
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