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

Title data

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. Vol. 39 (2013) Issue 3-4 . - pp. 391-422.
ISSN 1310-6600

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Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)264735-SADCO
Hermann Minkowski Center for Geometry at Tel-Aviv University, IsraelNo information

Project financing: 7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union
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Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: 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
Subject classification: Mathematics Subject Classification Code: 47H06 (54C65 47H04 54C60 26E25)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 19 Mar 2015 08:45
Last Modified: 04 Sep 2015 06:00
URI: https://eref.uni-bayreuth.de/id/eprint/8515

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