Differentiability of convex functions and the convex point of continuity property in Banach spaces

R. Deville; G. Godefroy; D. E. G. Hare; V. Zizler

doi:10.1007/BF02787266

Differentiability of convex functions and the convex point of continuity property in Banach spaces

R. Deville, G. Godefroy, D. E. G. Hare, V. Zizler

Research output: Contribution to journal › Article › peer-review

Abstract

We show that if X is a separable Banach space, then every continuous, convex, Gâteaux differentiable function on X is Fréchet differentiable on a dense set if and only if X* has the weak*-Convex Point of Continuity Property (C*PCP).

Original language	English (US)
Pages (from-to)	245-255
Number of pages	11
Journal	Israel Journal of Mathematics
Volume	59
Issue number	2
DOIs	https://doi.org/10.1007/BF02787266
State	Published - Jun 1987
Externally published	Yes

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title = "Differentiability of convex functions and the convex point of continuity property in Banach spaces",

abstract = "We show that if X is a separable Banach space, then every continuous, convex, G{\^a}teaux differentiable function on X is Fr{\'e}chet differentiable on a dense set if and only if X* has the weak*-Convex Point of Continuity Property (C*PCP).",

author = "R. Deville and G. Godefroy and Hare, {D. E. G.} and V. Zizler",

year = "1987",

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AU - Hare, D. E. G.

AU - Zizler, V.

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Differentiability of convex functions and the convex point of continuity property in Banach spaces

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