Gâteaux differentiability and uniform monotone approximation of convex functions in Banach spaces (Q2043689)
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scientific article; zbMATH DE number 7377539
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gâteaux differentiability and uniform monotone approximation of convex functions in Banach spaces |
scientific article; zbMATH DE number 7377539 |
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Gâteaux differentiability and uniform monotone approximation of convex functions in Banach spaces (English)
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3 August 2021
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Let \(X\) be a Banach space with \(X^\ast\) strictly convex. This interesting paper deals with the characterisation of convex coercive b-Lipschitzian functions \(f\) on \(X\). These are precisely, the uniform limits of sequences of convex, Gâteaux differentiable, coercive and b-Lipschitzian functions increasing from below \(f\) or decreasing from above \(f\). Here, b-Lipschitzian means Lipschitzian on bounded sets.
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uniform monotone approximation
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convex function
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strictly convex space
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Gâteaux differentiable
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0.832804799079895
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0.7991275787353516
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0.7822173237800598
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0.7789296507835388
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