Bulletin of the Australian Mathematical Society

Research Article

Lipschitz functions with maximal Clarke subdifferentials are staunch

Jonathan M. Borweina1 and Xianfu Wanga2

a1 Faculty of Computer Science, Dalhousie University 6050 University Avenue, Halifax, NS, Canada, B3H 1W5, e-mail: jborwein@cs.dal.ca

a2 Department of Mathematics and Statistics, UBC Okanagan, 3333 University Way, Kelowna, BC., Canada, V1V 1V7, e-mail: Shawn.Wang@ubc.ca

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.

(Received September 05 2005)