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Generic Fréchet Differentiability of Convex Functions on Non-Asplund Spaces

✍ Scribed by Cheng Lixin; Shi Shuzhong; E.S. Lee

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
204 KB
Volume
214
Category
Article
ISSN
0022-247X

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✦ Synopsis

Let f be a continuous convex function on a Banach space E. This paper shows that every proper convex function g on E with g F f is generically Frechet differentiable if and only if the image of the subdifferential map Ѩ f of f has the Radon᎐Nikodym property, and in this case it is equivalent to showing that the ímage of Ѩ f is separable on each separable subspace of E.

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