Bump functions and differentiability in Banach spaces (Q2750853)
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scientific article; zbMATH DE number 1663098
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bump functions and differentiability in Banach spaces |
scientific article; zbMATH DE number 1663098 |
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Bump functions and differentiability in Banach spaces (English)
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21 October 2001
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Asplund space
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subdifferential
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upper semincontinuous
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bump function
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0.96416783
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0.91184866
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0.91106117
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0.9071335
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0.9058582
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The result of \textit{R. Deville, G. Godefroy} and \textit{V. Zizler} [Mathematika 40, No. 2, 305-321 (1993; Zbl 0792.46007), Lemma III.6] that every Banach space admitting a pointwise Lipschitz Fréchet smooth bump function is Asplund is strengthened by weakening the assumption on the bump function to (upper semin)continuous symmetrically Fréchet subdifferentiable, i.e. NEWLINE\[NEWLINE\liminf_{h\to 0 }\frac{f(x+h)+f(x-h)-2f(x)}{\|h\|}\geq 0.NEWLINE\]
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