Geodesic
On Fréchet differentiability of convex functions on Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 249-253
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Equivalent conditions for the separability of the range of the subdifferential of a given convex Lipschitz function $f$ defined on a separable Banach space are studied. The conditions are in terms of a majorization of $f$ by a $C^1$-smooth function, separability of the boundary for $f$ or an approximation of $f$ by Fréchet smooth convex functions.
Equivalent conditions for the separability of the range of the subdifferential of a given convex Lipschitz function $f$ defined on a separable Banach space are studied. The conditions are in terms of a majorization of $f$ by a $C^1$-smooth function, separability of the boundary for $f$ or an approximation of $f$ by Fréchet smooth convex functions.
Classification : 46B03, 46G05, 49J50, 58C20
Keywords: Fréchet differentiability; convex functions; variational principles; Asplund spaces 
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     author = {Tang, Wee-Kee},
     title = {On {Fr\'echet} differentiability of convex functions on {Banach} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {249--253},
     year = {1995},
     volume = {36},
     number = {2},
     mrnumber = {1357526},
     zbl = {0831.46045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1995_36_2_a4/}
}
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Tang, Wee-Kee. On Fréchet differentiability of convex functions on Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 249-253. http://geodesic.mathdoc.fr/item/CMUC_1995_36_2_a4/