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Baier, Robert ; Farkhi, Elza:
Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity.
In: Serdica Mathematical Journal.
Bd. 39
(2013)
Heft 3-4
.
- S. 365-390.
ISSN 1310-6600
| Rez.: |
Dies ist die aktuelle Version des Eintrags.
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Angaben zu Projekten
| Projekttitel: |
Offizieller Projekttitel Projekt-ID Hermann Minkowski Center for Geometry Ohne Angabe Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO) 264735-SADCO |
|---|---|
| Projektfinanzierung: |
Hermann Minkowski Center for Geometry at Tel-Aviv University, Israel;
European Union "FP7-People-ITN" programme |
Abstract
We introduce Lipschitz continuity of set-valued maps with
respect to a given set difference. The existence of Lipschitz
selections that pass through any point of the graph of the map
and inherit its Lipschitz constant is studied. We show that the
Lipschitz property of the set-valued map with respect to the
Demyanov difference with a given constant is characterized by
the same property of its generalized Steiner selections.
For a univariate multifunction with only compact values in
$R^n$, we characterize its Lipschitz continuity
in the Hausdorff metric (with respect to the metric difference)
by the same property of its metric selections with the
same constant.
Weitere Angaben
| 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. Regularity Notions for Multimaps through Set Differences 3.1 Lipschitz Continuity 3.2 Properties and Hierarchy of Lipschitz Maps 4. Lipschitz Generalized Steiner Selections 5. Lipschitz Metric Selections 6. Examples 6.1 Examples for Different Lipschitz Notions 6.2 Examples for Lipschitz Selections Conclusions |
| Keywords: | Lipschitz continuous set-valued maps; selections; generalized Steiner selection; metric selection; set differences; Demyanov metric; Demyanov difference; metric difference |
| Fachklassifikationen: | Mathematics Subject Classification Code: 54C65 (54C60 26E25) |
| 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 |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 10 Feb 2015 07:45 |
| Letzte Änderung: | 23 Apr 2021 10:30 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/6652 |
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Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity. (deposited 07 Feb 2015 22:00)
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