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Nearest points to closed sets and directional derivatives of distance functions

Published online by Cambridge University Press:  17 April 2009

Simon Fitzpatrick
Simon Fitzpatrick
Affiliation:
Department of Mathematics and Statistics, University of Auckland, Auckland, New Zealand
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Abstract

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We investigate the circumstances under which the distance function to a closed set in a Banach space having a one-sided directional derivative equal to 1 or −1 implies the existence of nearest points. In reflexive spaces we show that at a dense set of points outside a closed set the distance function has a directional derivative equal to 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 2 , April 1989 , pp. 233 - 238
Copyright
Copyright © Australian Mathematical Society 1989

References

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