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The smooth variational principle and generic differentiability
Published online by Cambridge University Press: 17 April 2009
Abstract
A modified version of the smooth variational principle of Borwein and Preiss is proved. By its help it is shown that in a Banach space with uniformly Gâteaux differentiable norm every continuous function, which is directionally differentiable on a dense Gδ subset of the space, is Gâteaux differentiable on a dense Gδ subset of the space.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 43 , Issue 1 , February 1991 , pp. 169 - 175
- Copyright
- Copyright © Australian Mathematical Society 1991
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