Regularity of Set-Valued Maps and Their Selections through Set Differences. Part 2: One-Sided Lipschitz Properties
نویسندگان
چکیده
We introduce one-sided Lipschitz (OSL) conditions of set-valued 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 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.
منابع مشابه
Regularity of Set-Valued Maps and Their Selections through Set Differences. Part 1: Lipschitz Continuity
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 ge...
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