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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Yet more on the differentiability of convex functions


Author: John Rainwater
Journal: Proc. Amer. Math. Soc. 103 (1988), 773-778
MSC: Primary 46G05; Secondary 26B05, 46B22, 58C06, 90C48
MathSciNet review: 947656
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Abstract: Generic differentiability theorems are obtained for convex functions which are defined and locally Lipschitzian on the convex subset $ N(C)$ of nonsupport points of a closed convex subset $ C$ of a Banach space $ E$, which is assumed to be either an Asplund space (for Fréchet differentiability) or to be weakly compactly generated (for Gateaux differentiability).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0947656-7
PII: S 0002-9939(1988)0947656-7
Keywords: Convex functions, convex sets, support points, Asplund spaces, weak Asplund spaces, usco maps
Article copyright: © Copyright 1988 American Mathematical Society