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A farthest-point characterisation of the relative Chebyshev centre

Published online by Cambridge University Press:  17 April 2009

R. Huotari ,
M.P. Prophet  and
J. Shi
R. Huotari
Affiliation:
Utah State Universigy, Logan UT 84322-3900, United States of America
M.P. Prophet
Affiliation:
Murray State University, Murray KY 42071, United States of America
J. Shi
Affiliation:
Allianz Insurance Co, 3400 Riverside Dr, Suite 300, Burbank CA 91505, United States of America
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Abstract

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We characterise the relative Chebyshev centre of a compact subset F of a real Banach space in terms of the Gateaux derivative of the distance to farthest points. We present a relative-Chebyshev-centre characterisation of Hilbert space. In Hilbert space we show that the relative Chebyshev centre is in the closed convex hull of the metric projection of F, and we estimate the relative Chebyshev radius of F.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 1 , August 1996 , pp. 27 - 33
Copyright
Copyright © Australian Mathematical Society 1996

References

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