Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/3446

 Title: Regularity of Set-Valued Maps and Their Selections through Set Differences. Part 2: One-Sided Lipschitz Properties Authors: Baier, RobertFarkhi, Elza Keywords: one-sided Lipschitzian set-valued mapsselectionsgeneralized Steiner selectionmetric selectionset differencesDemyanov differencemetric 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. URI: http://hdl.handle.net/10525/3446 ISSN: 1310-6600 Appears in Collections: Volume 39, Number 3-4

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