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Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity

Abstract : We introduce Lipschitz continuity of set-valued maps with respect to a given set di erence. 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 di erence with a given constant is characterized by the same property of its generalized Steiner selections. For a univariate multifunction with only compact values in Rn, we characterize its Lipschitz continuity in the Hausdor metric (with respect to the metric di erence) by the same property of its metric selections with the same constant.
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https://hal.inria.fr/hal-01067206
Contributor : Estelle Bouzat <>
Submitted on : Tuesday, September 23, 2014 - 11:03:20 AM
Last modification on : Friday, October 13, 2017 - 5:08:16 PM

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Robert Baier, Elza Farkhi. Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity. Serdica Mathematical Journal, Bulgarian Academy of Sciences, 2013, Special volume dedicated to the 65th Anniversary of Professor Asen L. Dontchev and to the 60th Anniversary Professor Vladimir M. Veliov, 39 (3-4), pp.365-390. ⟨hal-01067206⟩

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