Geodesic
Semiconvex Functions: Representations as Suprema of Smooth Functions and Extensions
Journal of convex analysis, Tome 16 (2009) no. 1, pp. 239-26 Cet article a éte moissonné depuis la source Heldermann Verlag

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We prove results on representations of semiconvex functions with an arbitrary modulus (equivalently: strongly paraconvex functions) in superreflexive Banach spaces as suprema of families of differentiable functions. Also, results on extensions of semiconvex functions are proved. Further, characterizations of semiconvex functions by uniform Fréchet subdifferentiability and (global) [α]-subdifferentiability are given. We also show that weakly convex functions in Nurminskii's sense coincide with locally semiconvex functions.
Classification : 26B25, 46T99
Mots-clés : Semiconvex function, strongly paraconvex function, generalized subdifferentials, suprema of smooth functions 
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     author = {J. Duda and L. Zaj{\'\i}cek},
     title = {Semiconvex {Functions:} {Representations} as {Suprema} of {Smooth} {Functions} and {Extensions}},
     journal = {Journal of convex analysis},
     pages = {239--26},
     year = {2009},
     volume = {16},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a12/}
}
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J. Duda; L. Zajícek. Semiconvex Functions: Representations as Suprema of Smooth Functions and Extensions. Journal of convex analysis, Tome 16 (2009) no. 1, pp. 239-26. http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a12/