Gateaux and Hadamard Differentiability via Directional Differentiability

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10285323" target="_blank" >RIV/00216208:11320/14:10285323 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Gateaux and Hadamard Differentiability via Directional Differentiability
Original language description
Let X be a separable Banach space, Y a Banach space and f : X -> Y an arbitrary mapping. Then the following implication holds at each point x is an element of X except a sigma-directionally porous set: If the one-sided Hadamard directional derivative f(H+)'(x,u) exists in all directions u from a set S-x subset of X whose linear span is dense in X, then f is Hadamard differentiable at x. This theorem improves and generalizes a recent result of A. D. Ioffe, in which the linear span of S-x equals X and Y =R. An analogous theorem, in which f is pointwise Lipschitz, and which deals with the usual one-sided derivatives and Gateaux differentiability is also proved. It generalizes a result of D. Preiss and the author, in which f is supposed to be Lipschitz.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F12%2F0436" target="_blank" >GAP201/12/0436: Theory of Real Functions and Descriptive Set Theory III</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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