Geodesic
ε-Fréchet Differentiability of Lipschitz Functions and Applications
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 695-709

Voir la notice de l'article provenant de la source Heldermann Verlag

We study the ε-Fréchet differentiability of Lipschitz functions on Asplund generated Banach spaces. We prove a mean valued theorem and its equivalent, a formula for Clarke's subdifferential, in terms of this concept. We inspect proofs of several statements based on the deep Preiss's theorem on Fréchet differentiability of Lipschitz functions and we recognize that it is enough to use a simpler lemma on ε-Fréchet differentiability due to Fabian and Preiss. We do so for generic differentiability results of Giles and Sciffer, for the existence of nearest points of Borwein and Fitzpatrick, etc. We also show that the ε-Fréchet differentiability is separably reducible.
Classification : 46G05, 58C20, 49J50
Mots-clés : epsilon-Frechet differentiability, mean-value theorem, local epsilon-support, intermediate differentiability, Asplund generated space, boundedly Asplund set, separable reduction 
@article{JCA_2006_13_3_JCA_2006_13_3_a12,
     author = {M. Fabian and P. D. Loewen and X. Wang},
     title = {\ensuremath{\varepsilon}-Fr\'echet {Differentiability} of {Lipschitz} {Functions} and {Applications}},
     journal = {Journal of convex analysis},
     pages = {695--709},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2006},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a12/}
}
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M. Fabian; P. D. Loewen; X. Wang. ε-Fréchet Differentiability of Lipschitz Functions and Applications. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 695-709. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a12/