Title data
Baier, Robert ; Farkhi, Elza:
Regularity of setvalued maps and their selections through set differences. Part 2: Onesided Lipschitz properties.
In: Serdica Mathematical Journal.
Vol. 39
(2013)
Issue 34
.
 pp. 391422.
ISSN 13106600
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Project financing: 
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union Andere 
Abstract in another language
We introduce onesided Lipschitz (OSL) conditions of setvalued 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 convexvalued setvalued 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, onesided 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 Onesided Lipschitz conditions 3.2 Properties and relations between the different notions 4. Onesided Lipschitz selections 4.1 OSL generalized Steiner selections 4.2 Onesided Lipschitz metric selections 4.3 Onesided Lipschitz selections of OSL maps 5. Examples 5.1 Examples illustrating strict inclusions in Theorem 3.17 5.2 Examples of onesided Lipschitz selections Conclusions 
Keywords:  onesided Lipschitzian setvalued 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:  02 Jun 2021 10:02 
URI:  https://eref.unibayreuth.de/id/eprint/8515 
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Regularity of setvalued maps and their selections through set differences. Part 2: Onesided Lipschitz properties. (deposited 14 Mar 2015 22:00)
 Regularity of setvalued maps and their selections through set differences. Part 2: Onesided Lipschitz properties. (deposited 19 Mar 2015 08:45) [Currently Displayed]