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

URN to cite this document: urn:nbn:de:bvb:703-epub-1904-3

Title data

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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Project information

Project title:
Project's official titleProject's id
Hermann Minkowski Center for GeometryNo information
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)264735-SADCO

Project financing: 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.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): 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
Subject classification: Mathematics Subject Classification Code: 47H06 (54C65 47H04 54C60 26E25)
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-1904-3
Date Deposited: 09 Mar 2015 11:49
Last Modified: 28 Mar 2019 11:10
URI: https://epub.uni-bayreuth.de/id/eprint/1904

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