Title data
Baier, Robert ; Farkhi, Elza:
Regularity of setvalued maps and their selections through set differences. Part 1: Lipschitz continuity.
In: Serdica Mathematical Journal.
Vol. 39
(2013)
Issue 34
.
 pp. 365390.
ISSN 13106600
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Project information
Project title: 
Project's official title Project's id Hermann Minkowski Center for Geometry No information MarieCurie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO) 264735SADCO 

Project financing: 
Hermann Minkowski Center for Geometry at TelAviv University, Israel;
European Union "FP7PeopleITN" programme 
Abstract in another language
We introduce Lipschitz continuity of setvalued 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 setvalued 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.
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. 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 setvalued maps; selections; generalized Steiner selection; metric selection; set differences; Demyanov metric; Demyanov difference; metric difference 
Subject classification:  Mathematics Subject Classification Code: 54C65 (54C60 26E25) 
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 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  10 Feb 2015 07:45 
Last Modified:  23 Apr 2021 10:30 
URI:  https://eref.unibayreuth.de/id/eprint/6652 
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Regularity of setvalued maps and their selections through set differences. Part 1: Lipschitz continuity. (deposited 07 Feb 2015 22:00)
 Regularity of setvalued maps and their selections through set differences. Part 1: Lipschitz continuity. (deposited 10 Feb 2015 07:45) [Currently Displayed]