Abstract
We show that ifX is a separable Banach space, then every continuous, convex, Gâteaux differentiable function onX is Fréchet differentiable on a dense set if and only ifX* has theweak*-Convex Point of Continuity Property (C*PCP).
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Research completed while a visitor at the University of Alberta.
Research supported in part by an H. R. MacMillan Fellowship from the University of British Columbia.
Research partially supported by NSERC (Canada).
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Deville, R., Godefroy, G., Hare, D.E.G. et al. Differentiability of convex functions and the convex point of continuity property in Banach spaces. Israel J. Math. 59, 245–255 (1987). https://doi.org/10.1007/BF02787266
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DOI: https://doi.org/10.1007/BF02787266