Filling the gap between lower-C1 and lower-C2 functions

Aris Daniilidis, Jérôme Malick

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13 Citations (Scopus)


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-Holder 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 convex inequalities or via appropriate generalized monotonicity properties of their subdifferentials. Several examples are provided and a complete classification is given. © Heldermann Verlag.
Original languageEnglish
Pages (from-to)315-329
JournalJournal of Convex Analysis
Issue number2
Publication statusPublished - 1 Dec 2005


  • α-hypomonotone operator
  • α-weakly convex function
  • Lower-C function 1,α
  • Maximum function


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