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Generic Gateaux differentiability via smooth perturbations

Published online by Cambridge University Press:  17 April 2009

Pando Gr Georgiev  and
Nadia P. Zlateva
Pando Gr Georgiev
Affiliation:
Department of Mathematics and InformaticsUniversity of Sofia5 James Bourchier Blvd.1126 SofiaBulgaria
Nadia P. Zlateva
Affiliation:
Department of Mathematics and InformaticsUniversity of Sofia5 James Bourchier Blvd.1126 SofiaBulgaria
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Abstract

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We prove that in a Banach space with a Lipschitz uniformly Gateaux smooth bump function, every continuous function which is directionally differentiable on a dense Gδ subset of the space, is Gateaux differentiable on a dense Gδ subset of the space. Applications of this result are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 421 - 428
Copyright
Copyright © Australian Mathematical Society 1997

References

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