On Gâteaux Differentiability of Convex Functions in WCG Spaces

http://dx.doi.org/10.4153/CMB-2005-042-7
Canad. Math. Bull. 48(2005), 455-459

  Published:2005-09-01
 Printed: Sep 2005

It is shown, using the Borwein--Preiss variational principle that for every continuous convex function $f$ on a weakly compactly generated space $X$, every $x_0\in X$ and every weakly compact convex symmetric set $K$ such that $\cspan K=X$, there is a point of G\^ateaux differentiability of $f$ in $x_0+K$. This extends a Klee's result for separable spaces.