Geodesic
Differentiability of Approximately Convex, Semiconcave and Strongly Paraconvex Functions
Journal of convex analysis, Tome 15 (2008) no. 1, pp. 1-15 Cet article a éte moissonné depuis la source Heldermann Verlag

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It is shown that continuous approximately convex, semiconcave and strongly α( . )-paraconvex functions on Banach spaces have almost all (but not all) known first order differentiability properties of continuous convex functions. The main results easily follow from known (or essentially known) results on single-valuedness and continuity of submonotone operators.
Classification : 46G05, 49J50
Mots-clés : Approximately convex function, semiconcave function, strongly alpha-cdot-paraconvex function, submonotone operator, Frechet differentiability, Gateaux differentiability 
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     author = {L. Zaj{\'\i}cek},
     title = {Differentiability of {Approximately} {Convex,} {Semiconcave} and {Strongly} {Paraconvex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {1--15},
     year = {2008},
     volume = {15},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2008_15_1_JCA_2008_15_1_a0/}
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L. Zajícek. Differentiability of Approximately Convex, Semiconcave and Strongly Paraconvex Functions. Journal of convex analysis, Tome 15 (2008) no. 1, pp. 1-15. http://geodesic.mathdoc.fr/item/JCA_2008_15_1_JCA_2008_15_1_a0/