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Title: Regularity of Set-Valued Maps and Their Selections through Set Differences. Part 2: One-Sided Lipschitz Properties
Authors: Baier, Robert
Farkhi, Elza
Keywords: one-sided Lipschitzian set-valued maps
generalized Steiner selection
metric selection
set differences
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), 391p-422p
Abstract: We introduce one-sided 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 convex-valued set-valued 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 R^1 has OSL selections with the same OSL constant. For such a multifunction which is OSL with respect to the metric difference, one-sided Lipschitz metric selections exist through every point of its graph with the same OSL constant. 2010 Mathematics Subject Classification: 47H06, 54C65, 47H04, 54C60, 26E25.
ISSN: 1310-6600
Appears in Collections:Volume 39, Number 3-4

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