Geodesic
Fréchet directional differentiability and Fréchet differentiability
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 3, pp. 489-497 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 46G05, 58C20
Keywords: G\^ateaux and Fréchet subdifferentiability; directional differentiability; strict and intermediate differentiability 
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     author = {Giles, J. R. and Sciffer, Scott},
     title = {Fr\'echet directional differentiability and {Fr\'echet} differentiability},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {489--497},
     year = {1996},
     volume = {37},
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Giles, J. R.; Sciffer, Scott. Fréchet directional differentiability and Fréchet differentiability. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 3, pp. 489-497. http://geodesic.mathdoc.fr/item/CMUC_1996_37_3_a5/