A Construction of Convex Functions
Matematičeskie zametki, Tome 91 (2012) no. 1, pp. 74-78
Voir la notice de l'article provenant de la source Math-Net.Ru
We describe a construction of convex functions on infinite-dimensional spaces and apply this construction to give an illustration to a theorem of Borwein–Fabian from [1]. Namely, we give a simple explicit example of a continuous convex function on $l_p$, $p\ge 1$, which is everywhere compactly differentiable, but not Fréchet differentiable at zero.
Keywords:
topological vector space, normed space, convex function, Fréchet differentiability, Gâteaux differentiability, compact differentiability.
@article{MZM_2012_91_1_a6,
author = {T. Konderla},
title = {A {Construction} of {Convex} {Functions}},
journal = {Matemati\v{c}eskie zametki},
pages = {74--78},
publisher = {mathdoc},
volume = {91},
number = {1},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_1_a6/}
}
T. Konderla. A Construction of Convex Functions. Matematičeskie zametki, Tome 91 (2012) no. 1, pp. 74-78. http://geodesic.mathdoc.fr/item/MZM_2012_91_1_a6/