Title data
Baier, Robert ; Farkhi, Elza:
Regularity of setvalued maps and their selections through set differences. Part 2: Onesided Lipschitz properties.
Department of Mathematics, University of Bayreuth
Bayreuth, Germany
,
2013
.  29 S.


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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: 
Andere Hermann Minkowski Center for Geometry at TelAviv University, Israel; European Union "FP7PeopleITN" programme 
Abstract
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 IR^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:  Preprint, postprint 

Additional notes (visible to public):  erscheint in:
Serdica Mathematical Journal. Bd. 39 (2013) Heft 34 .  S. 391422. 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 Onesided Lipschitz conditions 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 for 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) 
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:703epub19043 
Date Deposited:  09 Mar 2015 11:49 
Last Modified:  02 Jun 2021 10:03 
URI:  https://epub.unibayreuth.de/id/eprint/1904 