Document Zbl 0511.41029

Centers and nearest points of sets. (English) Zbl 0511.41029

Proc. Am. Math. Soc. 85, 27-31 (1982).

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MSC:

41A45	Approximation by arbitrary linear expressions
41A50	Best approximation, Chebyshev systems
46B99	Normed linear spaces and Banach spaces; Banach lattices
46C99	Inner product spaces and their generalizations, Hilbert spaces

Keywords:

Cebysev center

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References:

[1]	Ivan Singer, Best approximation in normed linear spaces by elements of linear subspaces, Translated from the Romanian by Radu Georgescu. Die Grundlehren der mathematischen Wissenschaften, Band 171, Publishing House of the Academy of the Socialist Republic of Romania, Bucharest; Springer-Verlag, New York-Berlin, 1970. · Zbl 0197.38601
[2]	V. L. Klee, The review of a paper by N.A. Rutledge, Math. Rev. 13 (1952), 661.
[3]	Victor Klee, Circumspheres and inner products, Math. Scand. 8 (1960), 363 – 370. · Zbl 0100.31602 · doi:10.7146/math.scand.a-10618
[4]	A. L. Garkavi, On the Čebyšev center and convex hull of a set, Uspehi Mat. Nauk 19 (1964), no. 6 (120), 139 – 145 (Russian).
[5]	M. S. Brodskiĭ and D. P. Mil\(^{\prime}\)man, On the center of a convex set, Doklady Akad. Nauk SSSR (N.S.) 59 (1948), 837 – 840 (Russian).
[6]	J.-L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math. 20 (1967), 493 – 519. · Zbl 0152.34601 · doi:10.1002/cpa.3160200302
[7]	Joseph M. Lambert and Pierre D. Milman, Restricted Chebyshev centers of bounded subsets in arbitrary Banach spaces, J. Approx. Theory 26 (1979), no. 1, 71 – 78. · Zbl 0401.41037 · doi:10.1016/0021-9045(79)90133-3
[8]	Dan Amir and Frank Deutsch, Approximation by certain subspaces in the Banach space of continuous vector-valued functions, J. Approx. Theory 27 (1979), no. 3, 254 – 270. · Zbl 0426.41027 · doi:10.1016/0021-9045(79)90108-4
[9]	Heinrich Krüger, A remark on the lower semicontinuity of the set-valued metric projection, J. Approx. Theory 28 (1980), no. 1, 83 – 86. · Zbl 0428.41025 · doi:10.1016/0021-9045(80)90105-7
[10]	J. Borwein and L. Keener, The Hausdorff metric and Čebyšev centres, J. Approx. Theory 28 (1980), no. 4, 366 – 376. · Zbl 0461.41022 · doi:10.1016/0021-9045(80)90071-4
[11]	Frank Deutsch and Joseph M. Lambert, On continuity of metric projections, J. Approx. Theory 29 (1980), no. 2, 116 – 131. · Zbl 0514.41034 · doi:10.1016/0021-9045(80)90110-0
[12]	Jaroslav Mach, Continuity properties of Chebyshev centers, J. Approx. Theory 29 (1980), no. 3, 223 – 230. · Zbl 0467.41015 · doi:10.1016/0021-9045(80)90127-6
[13]	D. Amir and Z. Ziegler, Relative Chebyshev centers in normed linear spaces. I, J. Approx. Theory 29 (1980), no. 3, 235 – 252. · Zbl 0457.41031 · doi:10.1016/0021-9045(80)90129-X
[14]	Bruno Brosowski, Frank Deutsch, and Günther Nürnberger, Parametric approximation, J. Approx. Theory 29 (1980), no. 4, 261 – 277. · Zbl 0483.41033 · doi:10.1016/0021-9045(80)90115-X
[15]	Dan Amir, Chebyshev centers and uniform convexity, Pacific J. Math. 77 (1978), no. 1, 1 – 6. · Zbl 0361.46026
[16]	Ennio De Giorgi, Enrico Magenes, and Umberto Mosco , Proceedings of the International Meeting on Recent Methods in Nonlinear Analysis, Pitagora Editrice, Bologna, 1979.

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