## Chebyshev constant and Chebyshev points

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- by Susan L. Friedman PDF
- Trans. Amer. Math. Soc.
**186**(1973), 129-139 Request permission

## Abstract:

Using $\lambda$th power means in the case $\lambda \geq 1$, it is proven that the Chebyshev constant for any compact set in ${R_n}$, real Euclidean*n*-space, is equal to the radius of the spanning sphere. When $\lambda > 1$, the Chebyshev points of order

*m*for all $m \geq 1$ are unique and coincide with the center of the spanning sphere. For the case $\lambda = 1$, it is established that Chebyshev points of order

*m*for a compact set

*E*in ${R_2}$ are unique if and only if the cardinality of the intersection of

*E*with its spanning circle is greater than or equal to three.

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## Additional Information

- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**186**(1973), 129-139 - MSC: Primary 52A40
- DOI: https://doi.org/10.1090/S0002-9947-1973-0370365-6
- MathSciNet review: 0370365