Differentiability of convex functions and the convex point of continuity property in Banach spaces
type: Item
instance of: scholarly article
title: Differentiability of convex functions and the convex point of continuity property in Banach spaces
zbMATH Open document ID: 0654.46021
DOI: 10.1007/BF02787266
author: D. E. G. Hare
author: Robert Deville
author: Gilles Godefroy
author: V. Zizler
published in: Israel Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: It is shown that, for a separable Banach space X, every continuous convex Gateaux differentiable function on X is Fréchet differentiable on a dense set iff \(X^*\) has the weak*-convex point-of-continuity property (i.e. every weak*-compact convex subset of \(X^*\) has a point at which the relative weak* and norm topologies coincide).
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 58C20
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 4067600
zbMATH Keywords: Phelps space
zbMATH Keywords: Radon-Nikodym property
zbMATH Keywords: continuous convex Gateaux differentiable function
zbMATH Keywords: Fréchet differentiable on a dense set
zbMATH Keywords: weak*- convex point-of-continuity property
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4067600