The validity of the ``\(\liminf\)'' formula and a characterization of Asplund spaces (Q488770)
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scientific article; zbMATH DE number 6390686
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The validity of the ``\(\liminf\)'' formula and a characterization of Asplund spaces |
scientific article; zbMATH DE number 6390686 |
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The validity of the ``\(\liminf\)'' formula and a characterization of Asplund spaces (English)
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26 January 2015
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The authors address various topics related to the approximation of Clark's tangent and normal cones, using various bornologies on an ambient Banach space. Mostly, the space is assumed trustworthy in the sense of \textit{M. Fabian} [Acta Univ. Carol., Math. Phys. 30, No. 2, 51--56 (1989; Zbl 0714.49022)]. A new characterization of Asplund spaces, that uses the \(\lim\inf\) construction, is provided. Some criteria are given for the convexity of pseudo-convex sets.
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Clarke tangent cone
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Clarke normal cone
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Asplund spaces
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bornology
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Gâteaux derivative
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Fréchet derivative
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trustworthiness
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pseudoconvexity
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0.8731022
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0.87184936
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0.85557073
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0.8455805
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0.8453573
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