A class of strong differentiability spaces
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- by James B. Collier PDF
- Proc. Amer. Math. Soc. 53 (1975), 420-422 Request permission
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
- Edgar Asplund, Fréchet differentiability of convex functions, Acta Math. 121 (1968), 31–47. MR 231199, DOI 10.1007/BF02391908
- E. Asplund and R. T. Rockafellar, Gradients of convex functions, Trans. Amer. Math. Soc. 139 (1969), 443–467. MR 240621, DOI 10.1090/S0002-9947-1969-0240621-X
- R. R. Phelps, Dentability and extreme points in Banach spaces, J. Functional Analysis 17 (1974), 78–90. MR 0352941, DOI 10.1016/0022-1236(74)90005-6
- S. L. Troyanski, On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math. 37 (1970/71), 173–180. MR 306873, DOI 10.4064/sm-37-2-173-180
Additional Information
- © Copyright 1975 American Mathematical Society
- 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