Geodesic
Filling the Gap between Lower-C1 and Lower-C2 Functions
Journal of convex analysis, Tome 12 (2005) no. 2, pp. 315-329.

Voir la notice de l'article provenant de la source Heldermann Verlag

The classes of lower-$C^{1,\alpha}$ functions ($0\alpha\leq 1$), that is, functions locally representable as a maximum of a compactly parametrized family of continuously differentiable functions with $\alpha$-H\"{o}lder derivative, are hereby introduced. These classes form a strictly decreasing sequence from the larger class of lower-$C^1$ towards the smaller class of lower-$C^2$ 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.
Classification : 26B25, 49J52, 47H05
Mots-clés : Maximum function, lower-$C^{1,\alpha}$ function, $\alpha$-weakly convex function, $\alpha$-hypomonotone operator 
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     author = {A. Daniilidis and J. Malick},
     title = {Filling the {Gap} between {Lower-C\protect\textsuperscript{1}} and {Lower-C\protect\textsuperscript{2}} {Functions}},
     journal = {Journal of convex analysis},
     pages = {315--329},
     publisher = {mathdoc},
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     number = {2},
     year = {2005},
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A. Daniilidis; J. Malick. Filling the Gap between Lower-C1 and Lower-C2 Functions. Journal of convex analysis, Tome 12 (2005) no. 2, pp. 315-329. http://geodesic.mathdoc.fr/item/JCA_2005_12_2_JCA_2005_12_2_a4/