On Gateaux differentiability of pointwise Lipschitz mappings

الأصل · EN

We prove that for every function f:X→ Y, where X is a separable Banach space and Y is a Banach space with RNP, there exists a set A∈ such that f is Gateaux differentiable at all x∈ S(f) A, where S(f) is the set of points where f is pointwise-Lipschitz. This improves a result of Bongiorno. As a corollary, we obtain that every K-monotone function on a separable Banach space is Hadamard differentiable outside of a set belonging to; this improves a result due to Borwein and Wang. Another corollary is that if X is Asplund, f:X→ cone monotone, g:X→ continuous convex, then there exists a point in X, where f is Hadamard differentiable and g is Frechet differentiable.