Gâteaux and Hadamard differentiability via directional differentiability (Q2922470)
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scientific article; zbMATH DE number 6353706
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gâteaux and Hadamard differentiability via directional differentiability |
scientific article; zbMATH DE number 6353706 |
Statements
10 October 2014
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Hadamard derivative
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Gâteaux derivative
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directional derivative
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\(\sigma\)-directionally porous set
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pointwise Lipschitz mapping
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math.FA
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Gâteaux and Hadamard differentiability via directional differentiability (English)
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The author inspects the Gâteaux and Hadamard differentiablity as implied by directional differentiablity. The Ioffe result on the Hadamard differentiability is improved and generalized for vector-valued functions; cf. [\textit{A. Ioffe}, J. Convex Anal. 17, No. 3--4, 1019--1032 (2010; Zbl 1208.46043)].NEWLINENEWLINEAn analogous result on the connection between directional and Gâteaux derivatives is established, which generalizes a previous joint result by \textit{D. Preiss} and the author; see [Isr. J. Math. 125, 1--27 (2001; Zbl 1022.46026)].
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