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Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity

URN zum Zitieren dieses Dokuments: urn:nbn:de:bvb:703-epub-1851-2

Titelangaben

Baier, Robert ; Farkhi, Elza:
Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity.
Bayreuth , 2013 . - 24 S.

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baier_et_al_regularity_set-val_maps_part_1_2013.pdf - Preprint
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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 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: 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. 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)
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-1851-2
Eingestellt am: 06 Feb 2015 07:46
Letzte Änderung: 09 Mrz 2015 11:35
URI: https://epub.uni-bayreuth.de/id/eprint/1851