Fréchet directional differentiability and Fréchet differentiability
نویسندگان
چکیده
Zaj́ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any realvalued function on a normed linear space, the set of points where the function is Fréchet directionally differentiable but not Fréchet differentiable is first category.
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