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CHEBYSHEV SETS

Published online by Cambridge University Press:  11 November 2014

JAMES FLETCHER
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong 2522, Australia email jef336@uowmail.edu.au
WARREN B. MOORS*
Affiliation:
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand email moors@math.auckland.ac.nz
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Abstract

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A Chebyshev set is a subset of a normed linear space that admits unique best approximations. In the first part of this paper we present some basic results concerning Chebyshev sets. In particular, we investigate properties of the metric projection map, sufficient conditions for a subset of a normed linear space to be a Chebyshev set, and sufficient conditions for a Chebyshev set to be convex. In the second half of the paper we present a construction of a nonconvex Chebyshev subset of an inner product space.

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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