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On Gâteaux Differentiability of Convex Functions in WCG Spaces

  Published:2005-09-01
 Printed: Sep 2005
  • Jan Rychtář
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Abstract

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: Gâteaux smoothness, Borwein--Preiss variational principle, weakly compactly generated spaces Gâteaux smoothness, Borwein--Preiss variational principle, weakly compactly generated spaces
MSC Classifications: 46B20 show english descriptions Geometry and structure of normed linear spaces 46B20 - Geometry and structure of normed linear spaces
 

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