Title data
Baier, Robert ; Farkhi, Elza:
Regularity of setvalued maps and their selections through set differences. Part 1: Lipschitz continuity.
Bayreuth
,
2013
.  24 S.
PDF
baier_et_al_regularity_setval_maps_part_1_2013.pdf  Preprint Available under License Deutsches Urheberrechtsgesetz . Download (378kB) 
Project information
Project title: 



Project financing: 
Andere Hermann Minkowski Center for Geometry at TelAviv University, Israel; European Union "FP7PeopleITN" programme 
Abstract
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:  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. 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) 
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:703epub18512 
Date Deposited:  06 Feb 2015 07:46 
Last Modified:  28 Mar 2019 10:36 
URI:  https://epub.unibayreuth.de/id/eprint/1851 