Geodesic
The relative Chebyshev center of a finite set in a geodesic space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2008), pp. 66-72.

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In the present paper we estimate variation in the relative Chebyshev radius $R_W(M)$, where $M$ and $W$are nonempty bounded sets of a metric space, as the sets $M$ and $W$ change. We find the closure and the interior of the set of all $N$-nets each of which contains its unique relative Chebyshev center, in the set of all $N$-nets of a special geodesic space endowed by the Hausdorff metric. We consider various properties of relative Chebyshev centers of a finite set which lie in this set.
Keywords: relative Chebyshev center, Hausdorff metric, geodesic space. 
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E. N. Sosov. The relative Chebyshev center of a finite set in a geodesic space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2008), pp. 66-72. http://geodesic.mathdoc.fr/item/IVM_2008_4_a6/

[1] Garkavi A. L., “O nailuchshei seti i nailuchshem sechenii mnozhestv v normirovannom prostranstve”, Izv. AN SSSR. Ser. matem., 26:1 (1962), 87–106 | MR

[2] Kuratovskii K., Topologiya, T. 1, Mir, M., 1966, 594 pp. | MR

[3] Wisnicki A., Wosko J., “On relative Hausdorff measures of noncompactness and relative Chebyshev radii in Banach spaces”, Proc. Amer. Math. Soc., 124:8 (1996), 2465–2474 | DOI | MR | Zbl

[4] Amir D., Mach J., Saatkamp K., “Existence of Chebyshev centers, best $n$-nets and best compact approximants”, Trans. Amer. Math. Soc., 271:2 (1982), 513–524 | DOI | MR | Zbl

[5] Khamsi M. A., “On metric spaces with uniform normal structure”, Proc. Amer. Math. Soc., 106:3 (1989), 723–726 | DOI | MR | Zbl

[6] Buzeman G., Geometriya geodezicheskikh, Fizmatgiz, M., 1962, 503 pp. | MR

[7] Papadopoulos A., Metric spaces convexity and nonpositive curvature, European Math. Society, Zurich, 2005, 287 pp. | MR

[8] Burago D. Yu., Burago Yu. D., Ivanov S. V., Kurs metricheskoi geometrii, In-t kompyuternykh issledovanii, Moskva–Izhevsk, 2004, 496 pp. | MR

[9] Buyalo S., Schroeder V., “Extension of Lipschitz maps into $3$-manifolds”, Asian J. Math., 5:4 (2001), 685–704 | MR | Zbl