Journal of Convex Analysis 27 (2020), No. 2, 753--776
Copyright Heldermann Verlag 2020
Lipschitz-like Property of Subdifferential Mapping of Convex Continuous Functions on Hilbert Space
Dariusz Zagrodny
University of Lodz, Faculty of Mathematics and Computer Science, Lodz, Poland
dariusz.zagrodny@wmii.uni.lodz.pl
A Lipschitz-like property of subdifferential mappings of convex continuous functions on Hilbert spaces is investigated. It is shown that the subdifferential mapping of such a function admits a Lipschitz-like property at all points from a dense subset of its domain. In particular, Lipschitz-like properties of subdifferentials of distance functions from sets with convex complements are discovered.
Keywords: Convex functions, Aubin Lipschitz-like properties, best approximation, metric projection mapping, Borel sets.
MSC: 52A41; 49J50.
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