Regularity of Set-Valued Maps and their Selections through Set Differences. Part 1: Lipschitz Continuity

Baier, Robert, and Farkhi, Elza. "Regularity of Set-Valued Maps and their Selections through Set Differences. Part 1: Lipschitz Continuity." Serdica Mathematical Journal 39.3-4 (2013): 365-390. <http://eudml.org/doc/294989>.

@article{Baier2013,
abstract = {We introduce Lipschitz continuity of set-valued 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 set-valued 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. 2010 Mathematics Subject Classification: 54C65, 54C60, 26E25.},
author = {Baier, Robert, Farkhi, Elza},
journal = {Serdica Mathematical Journal},
keywords = {Lipschitz continuous set-valued maps; selections; generalized Steiner selection; metric selection; set differences; Demyanov metric; Demyanov difference; metric difference},
language = {eng},
number = {3-4},
pages = {365-390},
publisher = {Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences},
title = {Regularity of Set-Valued Maps and their Selections through Set Differences. Part 1: Lipschitz Continuity},
url = {http://eudml.org/doc/294989},
volume = {39},
year = {2013},
}

TY - JOUR
AU - Baier, Robert
AU - Farkhi, Elza
TI - Regularity of Set-Valued Maps and their Selections through Set Differences. Part 1: Lipschitz Continuity
JO - Serdica Mathematical Journal
PY - 2013
PB - Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
VL - 39
IS - 3-4
SP - 365
EP - 390
AB - We introduce Lipschitz continuity of set-valued 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 set-valued 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. 2010 Mathematics Subject Classification: 54C65, 54C60, 26E25.
LA - eng
KW - Lipschitz continuous set-valued maps; selections; generalized Steiner selection; metric selection; set differences; Demyanov metric; Demyanov difference; metric difference
UR - http://eudml.org/doc/294989
ER -