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Duality and subdifferential for convex functions on complete metric spaces

✍ Scribed by Bijan Ahmadi Kakavandi; Massoud Amini

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
279 KB
Volume
73
Category
Article
ISSN
0362-546X

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Duality and subdifferential for convex f
Duality and subdifferential for convex functions on complete metric spaces
✍ Bijan Ahmadi Kakavandi; Massoud Amini πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 279 KB

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

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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 Γ— E \* ) for the E ros-Borel structures. We also prove that th

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## Abstract In this paper we work in separated locally convex spaces where we give equivalent statements for the formulae of the conjugate function of the sum of a convex lower‐semicontinuous function and the precomposition of another convex lower‐semicontinuous function which is also __K__ ‐increa