Reference for Chebyshev centers

Question

Today, I came across the concept of Chebyshev center twice.

In particular, it is the key tool in the very elegant paper "A fixed point theorem for $L^1$ spaces" by Bader, Gelander and Monod.

Why is this concept named after Chebyshev?

Answer 1

The name "Chebyshev center" was introduced by Garkavi [1], for the relationship to the Cheybshev approximation problem (minimize the maximum error). Garkavi refers to a 1951 paper by Zukhovitskii for this connection [2].

_{An important special case of the problem of the best $N$-network is the problem of the smallest sphere containing a given set (i.e., the case $N=1$). We will call the center of the smallest sphere containing the set $M$ the Chebyshev center of this set [cf. (2), (8)].}

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[1] A. L. Garkavi, On the optimal net and best cross-section of a set in a normed space, Izv. Akad. Nauk SSSR Ser. Mat., 1962, Volume 26, Issue 1, 87–106.

[2] S.I. Zukhovitskii, Algorithm for finding the point that least deviates (in the sense of Chebyshev) from a given system of $n$ points, Reports Ak. Sciences of the Ukrainian SSR, 6 (1951), 404-407.