## On Fréchet differentiability of convex functions on Banach spaces.(English)Zbl 0831.46045

Summary: 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.

### MSC:

 46G05 Derivatives of functions in infinite-dimensional spaces 49J50 Fréchet and Gateaux differentiability in optimization 46B03 Isomorphic theory (including renorming) of Banach spaces
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