1. CMB 2005 (vol 48 pp. 455)
|On GÃ¢teaux Differentiability of Convex Functions in WCG Spaces |
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.
Keywords:GÃ¢teaux smoothness, Borwein--Preiss variational principle,, weakly compactly generated spaces