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

Published online by Cambridge University Press:  20 November 2018

J. M. Borwein*
Affiliation:
Department of Combinatorics and Optimization University of Waterloo, Waterloo, Ontario N2L 3G1
M. Fabian*
Affiliation:
Department of Mathematics Faculty of Machine Engineering Czech Technical University12800 Prague 2 Czechoslovakia
*
Current address: Department of Mathematics and Statistics Simon Fraser University Burnaby, British Columbia V5A 1S6
Current address: Department of Mathematics and Statistics Simon Fraser University Burnaby, British Columbia V5A 1S6
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1993

References

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