γ-Subdifferential and γ-convexity of functions on a normed space
✍ Scribed by H. X. Phu
- Publisher
- Springer
- Year
- 1995
- Tongue
- English
- Weight
- 907 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0022-3239
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Thanks to the recent concept of quasilinearization of Berg and Nikolaev, we have introduced the notion of duality and subdifferential on complete CAT (0) (Hadamard) spaces. For a Hadamard space X , its dual is a metric space X \* which strictly separates non-empty, disjoint, convex closed subsets o
Let E be a separable Banach space with separable dual. We show that the operation of subdi erentiation and the inverse operation are Borel from the convex functions on E into the monotone operators on E (subspace of the closed sets of E × E \* ) for the E ros-Borel structures. We also prove that th