On Gâteaux Differentiability of Convex Functions in WCG Spaces
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
there is a point of G\^ateaux differentiability of $f$ in $x_0+K$.
This extends a Klee's result for separable spaces.
Gâteaux smoothness, Borwein--Preiss variational principle, weakly compactly generated spaces
46B20 - Geometry and structure of normed linear spaces