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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Chebyshev constant for centered sets


Author: Susan L. Friedman
Journal: Proc. Amer. Math. Soc. 50 (1975), 344-350
MSC: Primary 41A45
MathSciNet review: 0370015
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Abstract: Using $ \lambda $th power means in the case $ \lambda \geq 1$ it is proven that the Chebyshev constant of any bounded centered set in a metric space is equal to one-half the topological diameter of the set. Thus the Chebyshev constant for any unit ball of a normed linear space is equal to one for the above means.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0370015-6
Article copyright: © Copyright 1975 American Mathematical Society