Zaj'\i ček 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 real-valued function on a normed linear space, the set of points where the function is Fréchet directionally differentiable but not Fréchet differentiable is first category.
@article{118855,
author = {John R. Giles and Scott Sciffer},
title = {Fr\'echet directional differentiability and Fr\'echet differentiability},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {37},
year = {1996},
pages = {489-497},
zbl = {0881.58011},
mrnumber = {1426913},
language = {en},
url = {http://dml.mathdoc.fr/item/118855}
}
Giles, John R.; Sciffer, Scott. Fréchet directional differentiability and Fréchet differentiability. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 489-497. http://gdmltest.u-ga.fr/item/118855/
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