Chebyshev constant and Chebyshev points

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.