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Filling the Gap Between Lower-C1 and Lower-C2 Functions

Abstract : The classes of lower-C1,α functions (0 < α ≤ 1), that is, functions locally representable as a maximum of a compactly parametrized family of continuously differentiable functions with α-H ̈older derivative, are hereby introduced. These classes form a strictly decreasing sequence from the larger class of lower-C1 towards the smaller class of lower-C2 functions, and can be analogously characterized via perturbed con- vex inequalities or via appropriate generalized monotonicity properties of their subdifferentials. Several examples are provided and a complete classification is given.
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https://hal.inria.fr/hal-00804407
Contributor : Jérôme Malick <>
Submitted on : Monday, March 25, 2013 - 2:35:04 PM
Last modification on : Monday, March 29, 2021 - 11:50:03 AM
Long-term archiving on: : Wednesday, June 26, 2013 - 4:02:29 AM

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Aris Daniilidis, Jérôme Malick. Filling the Gap Between Lower-C1 and Lower-C2 Functions. Journal of Convex Analysis, Heldermann, 2005, 12 (2), pp.315-329. ⟨hal-00804407⟩

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