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
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