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Title: Regularity of Set-Valued Maps and their Selections through Set Differences. Part 1: Lipschitz Continuity
Authors: Baier, Robert
Farkhi, Elza
Keywords: Lipschitz continuous set-valued maps
generalized Steiner selection
metric selection
set differences
Demyanov metric
Demyanov difference
metric difference
Issue Date: 2013
Publisher: Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 39, No 3-4, (2013), 365p-390p
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.
ISSN: 1310-6600
Appears in Collections:Volume 39, Number 3-4

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