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On Convex Functions Having Points of Gateaux Differentiability Which are Not Points of Fréchet Differentiability

  • J. M. Borwein (a1) and M. Fabian (a2)
Abstract

We study the relationships between Gateaux, Fréchet and weak Hadamard differentiability of convex functions and of equivalent norms. As a consequence we provide related characterizations of infinite dimensional Banach spaces and of Banach spaces containing ł1. Explicit examples are given. Some renormings of WCG Asplund spaces are made in this vein.

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Corresponding author
Current address: Department of Mathematics and Statistics Simon Fraser University Burnaby, British Columbia V5A 1S6
References
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[B] Borwein, J.M., Asplund spaces are ‘Sequentially reflexive ‘ , preprint.
[BFa] Borwein, J.M. and Fabian, M., On convex functions having points of Gateaux differentiability which are not points of Fréchet differentiability , Technical Report, University of Waterloo CORR 92-04, February 1992.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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