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Continuity characterisations of differentiability of locally Lipschitz functions

Published online by Cambridge University Press:  17 April 2009

J.R. Giles  and
Scott Sciffer
J.R. Giles
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle NSW 2308
Scott Sciffer
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle NSW 2308
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Recently David Preiss contributed a remarkable theorem about the differentiability of locally Lipschitz functions on Banach spaces which have an equivalent norm differentiable away from the origin. Using his result in conjunction with Frank Clarke's non-smooth analysis for locally Lipschitz functions, continuity characterisations of differentiability can be obtained which generalise those for convex functions on Banach spaces. This result gives added information about differentiability properties of distance functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 3 , June 1990 , pp. 371 - 380
Copyright
Copyright © Australian Mathematical Society 1990

References

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