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Gateaux differentiable functions are somewhere Fréchet differentiable. (English) Zbl 0573.46024
Let G be a nonempty open subset of an Asplund space (i.e. such real Banach space, all of whose separable subspaces have a separable dual) and let \(f: G\to {\mathbb{R}}\) be locally Lipschitz and Gâteaux differentiable at every point of G. Then the author has proved that f is Fréchet differentiable at uncountably many points of G. The nonseparable case is reduced to the separable one with the help of a general separable reduction theorem.
Reviewer: Duong Minh Duc

MSC:
46G05 Derivatives of functions in infinite-dimensional spaces
46B22 Radon-Nikodým, Kreĭn-Milman and related properties
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