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Proceedings of the American Mathematical Society

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A class of strong differentiability spaces


Author: James B. Collier
Journal: Proc. Amer. Math. Soc. 53 (1975), 420-422
MSC: Primary 46B05
DOI: https://doi.org/10.1090/S0002-9939-1975-0388044-5
MathSciNet review: 0388044
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Abstract: It is shown that if the dual of a Banach space $ X$ is weakly compactly generated, then each convex function on $ X$ is Fréchet differentiable on a dense $ {G_\delta }$ subset of its domain of continuity.


References [Enhancements On Off] (What's this?)

  • [1] E. Asplund, Fréchet differentiability of convex functions, Acta Math. 121 (1968), 31-47. MR 37 #6754. MR 0231199 (37:6754)
  • [2] E. Asplund and R. T. Rockafellar, Gradients of convex functions, Trans. Amer. Math. Soc. 139 (1969), 443-467. MR 39 #1968. MR 0240621 (39:1968)
  • [3] R. R. Phelps, Dentability and extreme points in Banach spaces, J. Functional Anal. 17 (1974), 78-90. MR 0352941 (50:5427)
  • [4] S. L. Trojanski, On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math. 37 (1970/71), 173-180. MR 46 #5995. MR 0306873 (46:5995)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0388044-5
Keywords: Fréchet differentiability, convex function, strongly exposed point
Article copyright: © Copyright 1975 American Mathematical Society

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