4 Mar
2018
4 Mar
'18
3:57 p.m.
This is an announcement for the paper “GÂteaux-Differentiability of Convex Functions in Infinite Dimension” by Mohammed Bachirhttps://arxiv.org/find/math/1/au:+Bachir_M/0/1/0/all/0/1 (UP1), Adrien Fabrehttps://arxiv.org/find/math/1/au:+Fabre_A/0/1/0/all/0/1.
Abstract: It is well known that in $R^n$ , G{^a}teaux (hence Fr{'e}chet) differ-entiability of a convex continuous function at some point is equivalent to the existence of the partial derivatives at this point. We prove that this result extends naturally to certain infinite dimensional vector spaces, in particular to Banach spaces having a Schauder basis.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1802.07633