On Gâteaux Differentiability of Convex Functions in WCG Spaces

• Autores: Jan Rychtár
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 3, 2005, págs. 455-459
• Idioma: inglés
• DOI: 10.4153/cmb-2005-042-7
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• Resumen

  • It is shown, using the Borwein¿Preiss variational principle that for every continuous convex function f on a weakly compactly generated space X, every x0 ? X and every weakly compact convex symmetric set K such that \cspan K = X, there is a point of Gâteaux differentiability of f in x0 + K. This extends a Klee's result for separable spaces.