More on the differentiability of convex functions

Author:
Maria Elena Verona

Journal:
Proc. Amer. Math. Soc. **103** (1988), 137-140

MSC:
Primary 58C20; Secondary 26B25, 49A51, 90C25

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938657-3

MathSciNet review:
938657

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a closed, convex set in a topological vector space such that , the set of its nonsupport points, is nonempty (this is always the case if is Banach separable; if is Fréchet, is residual in ). If is normed, we prove that any locally Lipschitz, convex real function on is subdifferentiable on . If in addition is Banach separable, we prove that is smooth on a residual subset of .

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0938657-3

Article copyright:
© Copyright 1988
American Mathematical Society