Centers and nearest points of sets
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- by P. Szeptycki and F. S. Van Vleck PDF
- Proc. Amer. Math. Soc. 85 (1982), 27-31 Request permission
Abstract:
For a Banach space $X$ and a subset $A$ of $X$, ${c_A}$ denotes the Čebyšev center of $A$ and ${P_A}x$ denotes the nearest point in $A$ to the point $x$ in $X$. The space of all subsets of $X$ is furnished with the Hausdorff metric. The modulus of continuity of the function $A \to {c_A}$ is computed in the case when $X$ is a Hilbert space and the sets $A$ are compact; the same is done for the function $A \to {P_A}x$, for fixed $x$, in the case when $X$ is uniformly convex and the sets $A$ are convex and closed.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- 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