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The smooth variational principle and generic differentiability

Published online by Cambridge University Press:  17 April 2009

Pando Grigorov Georgiev
Pando Grigorov Georgiev
Affiliation:
University of Sofia, Department of Mathematics and Informatics, 5 “Anton Ivanov” Boul., Sofia 1126, Bulgaria
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Abstract

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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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