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On Fréchet differentiability of convex functions on Banach spaces

Wee-Kee Tang (1995)

Commentationes Mathematicae Universitatis Carolinae

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.

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