Centers and nearest points of sets

Authors:
P. Szeptycki and F. S. Van Vleck

Journal:
Proc. Amer. Math. Soc. **85** (1982), 27-31

MSC:
Primary 46B99; Secondary 41A65

DOI:
https://doi.org/10.1090/S0002-9939-1982-0647891-6

MathSciNet review:
647891

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Abstract | References | Similar Articles | Additional Information

Abstract: For a Banach space and a subset of , denotes the Čebyšev center of and denotes the nearest point in to the point in . The space of all subsets of is furnished with the Hausdorff metric. The modulus of continuity of the function is computed in the case when is a Hilbert space and the sets are compact; the same is done for the function , for fixed , in the case when is uniformly convex and the sets are convex and closed.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1982-0647891-6

Keywords:
Čebyšev center,
nearest point,
modulus of continuity

Article copyright:
© Copyright 1982
American Mathematical Society