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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.
Department of Mathematics, University of Bayreuth
Bayreuth, Germany
,
2013
. - 29 S.
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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 |
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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.
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| Publikationsform: | Preprint, Postprint |
|---|---|
| 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 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) |
| 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: | 14 Mär 2015 22:00 |
| Letzte Änderung: | 16 Mär 2015 07:27 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/8376 |
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