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Gateaux Differentiability of Convex Functions on Banach Spaces

✍ Scribed by Larman, D. G.; Phelps, R. R.


Book ID
120096748
Publisher
Oxford University Press
Year
1979
Tongue
English
Weight
331 KB
Volume
s2-20
Category
Article
ISSN
0024-6107

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Generic Fréchet Differentiability of Con
✍ Cheng Lixin; Shi Shuzhong; E.S. Lee 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 204 KB

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 show