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Lipschitz functions with maximal Clarke subdifferentials are staunch

Published online by Cambridge University Press:  17 April 2009

Jonathan M. Borwein  and
Xianfu Wang
Jonathan M. Borwein
Affiliation:
Faculty of Computer Science, Dalhousie University 6050 University Avenue, Halifax, NS, Canada, B3H 1W5, e-mail: jborwein@cs.dal.ca
Xianfu Wang
Affiliation:
Department of Mathematics and Statistics, UBC Okanagan, 3333 University Way, Kelowna, BC., Canada, V1V 1V7, e-mail: Shawn.Wang@ubc.ca
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In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire's category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only generic, but also staunch in the space of non-expansive functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 3 , December 2005 , pp. 491 - 496
Copyright
Copyright © Australian Mathematical Society 2005

References

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