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Separable determination of Fréchet differentiability of convex functions

Published online by Cambridge University Press:  17 April 2009

J.R. Giles  and
Scott Sciffer
J.R. Giles
Affiliation:
Department of MathematicsThe University of NewcastleNewcastle NSW 2308
Scott Sciffer
Affiliation:
Department of MathematicsThe University of NewcastleNewcastle NSW 2308
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Abstract

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For a continuous convex function on an open convex subset of any Banach space a separability condition on its image under the subdifferential mapping is sufficient to guarantee the generic Fréchet differentiability of the function. This gives a direct insight into the characterisation of Asplund spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 1 , August 1995 , pp. 161 - 167
Copyright
Copyright © Australian Mathematical Society 1995

References

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