Global approximation of convex functions by differentiable convex functions on Banach spaces (Q2789241)
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scientific article; zbMATH DE number 6546687
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global approximation of convex functions by differentiable convex functions on Banach spaces |
scientific article; zbMATH DE number 6546687 |
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26 February 2016
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convex function
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locally rotund norm
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differentiable function
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math.FA
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Global approximation of convex functions by differentiable convex functions on Banach spaces (English)
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Let \(U\) be an open convex subset of a Banach space \(X\) such that \(X^*\) has a locally uniform rotund norm. Then, given \(\varepsilon \geq 0\) and a continuous convex function \(f:U\to \mathbb R\), there is a continuously differentiable convex function \(g:U\to \mathbb R\) such that \(f-\varepsilon\leq g\leq f\) on \(U\).
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