Differentiability of convex functions and the convex point of continuity property in Banach spaces (Q1108539)
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scientific article; zbMATH DE number 4067600
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Differentiability of convex functions and the convex point of continuity property in Banach spaces |
scientific article; zbMATH DE number 4067600 |
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Differentiability of convex functions and the convex point of continuity property in Banach spaces (English)
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1987
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It is shown that, for a separable Banach space X, every continuous convex Gateaux differentiable function on X is Fréchet differentiable on a dense set iff \(X^*\) has the weak*-convex point-of-continuity property (i.e. every weak*-compact convex subset of \(X^*\) has a point at which the relative weak* and norm topologies coincide).
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Phelps space
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Radon-Nikodym property
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continuous convex Gateaux differentiable function
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Fréchet differentiable on a dense set
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weak*- convex point-of-continuity property
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