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Farthest points and monotone operators

Published online by Cambridge University Press:  17 April 2009

U. Westphal  and
T. Schwartz
U. Westphal
Affiliation:
Institut für Mathematik, Universität Hannover, Welfengarten 1, 30167 HannoverGermany e-mail: westphal@math.uni-hannover.de, schwartz@math.uni-hannover.de
T. Schwartz
Affiliation:
Institut für Mathematik, Universität Hannover, Welfengarten 1, 30167 HannoverGermany e-mail: westphal@math.uni-hannover.de, schwartz@math.uni-hannover.de
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Abstract

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We apply the theory of monotone operators to study farthest points in closed bounded subsets of real Banach spaces. This new approach reveals the intimate connection between the farthest point mapping and the subdifferential of the farthest distance function. Moreover, we prove that a typical exception set in the Baire category sense is pathwise connected. Stronger results are obtained in Hilbert spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 1 , August 1998 , pp. 75 - 92
Copyright
Copyright © Australian Mathematical Society 1998

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