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On Gâteaux Differentiability of Convex Functions in WCG Spaces
Published online by Cambridge University Press: 20 November 2018
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 $\overline{\text{span}}K=X$, there is a point of Gâteaux differentiability of $f$ in ${{x}_{0}}+K$. This extends a Klee's result for separable spaces.
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- Copyright © Canadian Mathematical Society 2005
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