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On Gâteaux Differentiability of Convex Functions in WCG Spaces

Published online by Cambridge University Press:  20 November 2018

Jan Rychtář
Jan Rychtář*
Affiliation:
Department of Mathematical Sciences, University of North Carolina at Greensboro, Greensboro, NC 27402, U.S.A. e-mail: rychtar@uncg.edu
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Abstract

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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.

Keywords

46B20Gâteaux smoothnessBorwein–Preiss variational principleweakly compactly generated spaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 3 , 01 September 2005 , pp. 455 - 459
Copyright
Copyright © Canadian Mathematical Society 2005

References

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