On differentiability properties of Lipschitz functions on a Banach space with a Lipschitz uniformly Gâteaux differentiable bump function
Zajíček, Luděk
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 329-336 / Harvested from Czech Digital Mathematics Library
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We improve a theorem of P.G. Georgiev and N.P. Zlateva on G\^ateaux differentiability of Lipschitz functions in a Banach space which admits a Lipschitz uniformly G\^ateaux differentiable bump function. In particular, our result implies the following theorem: If $d$ is a distance function determined by a closed subset $A$ of a Banach space $X$ with a uniformly G\^ateaux differentiable norm, then the set of points of $X\setminus A$ at which $d$ is not G\^ateaux differentiable is not only a first category set, but it is even $\sigma$-porous in a rather strong sense.

Publié le : 1997-01-01
Classification:  41A65,  46B20,  46G05 
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     author = {Lud\v ek Zaj\'\i \v cek},
     title = {On differentiability properties of Lipschitz functions on a Banach space with a Lipschitz uniformly G\^ateaux differentiable bump function},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {329-336},
     zbl = {0886.46049},
     mrnumber = {1455499},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118930}
}

Zajíček, Luděk. On differentiability properties of Lipschitz functions on a Banach space with a Lipschitz uniformly Gâteaux differentiable bump function. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 329-336. http://gdmltest.u-ga.fr/item/118930/

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