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Papini, Pier Luigi; Singer, Ivan

Best coapproximation in normed linear spaces. (English) Zbl 0421.41017

Monatsh. Math. 88, 27-44 (1979).
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Cited in 3 Reviews
Cited in 27 Documents

MSC:

41A50 Best approximation, Chebyshev systems
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Keywords:

normed linear spaces; elements of best coapproximation; spaces of continuous functions
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\textit{P. L. Papini} and \textit{I. Singer}, Monatsh. Math. 88, 27--44 (1979; Zbl 0421.41017)
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References:

[1] Birkhoff, G.: Orthogonality in linear metric spaces. Duke Math. J. 1, 169-172 (1935). · Zbl 0012.30604
[2] Bruck, Jr., R. E.: Nonexpansive projections on subsets of Banach spaces. Pacific J. Math. 47, 341-355 (1973). · Zbl 0274.47030
[3] Cheney, E. W., andK. H. Price: Minimal projections. In: Approximation Theory (Ed.A. Talbot), p. 261-289. New York: Academic Press. 1970. · Zbl 0217.16202
[4] Day, M. M.: Review of the paper ofJ. R. Holub ?Rotundity, orthogonality and characterizations of inner product spaces?. Math. Rev. 52, 175 (1976) ? 1263.
[5] Franchetti, C., andM. Furi: Some characteristic properties of real Hilbert spaces. Rev. Roumaine Math. Pures Appl. 17, 1045-1048 (1972). · Zbl 0245.46024
[6] Holub, J. R.: Rotundity, orthogonality and characterizations of inner product spaces. Bull. Amer. Math. Soc. 81, 1087-1089 (1975). · Zbl 0317.46022
[7] James, R. C.: Orthogonality and linear functionals in normed linear spaces. Trans. Amer. Math. Soc. 61, 265-292 (1947). · Zbl 0037.08001
[8] Lazar, A., andM. Zippin: On finite-dimensional subspaces of Banach spaces. Israel J. Math. 3, 147-156 (1965). · Zbl 0143.35001
[9] Lindenstrauss, J.: On projections with norm 1 ? an example. Proc. Amer. Math. Soc. 15, 403-406 (1964). · Zbl 0125.06601
[10] Papini, P. L.: Some questions related to the concept of orthogonality in Banach spaces. Proximity maps; bases. Boll. Un. Mat. Ital. (4) 11, 44-63 (1975). · Zbl 0321.46014
[11] Papini, P. L.: Approximation and strong approximation in normed spaces via tangent functionals. J. Approx. Theory 22, 111-118 (1978). · Zbl 0377.41024
[12] Singer, I.: Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces. Bucharest: Publ. House Acad. and Berlin-Heidelberg-New York: Springer. 1970. · Zbl 0197.38601
[13] Singer, I.: The theory of best approximation and functional analysis. CBMS Reg. Conf. Ser. Appl. Math. 13. Philadelphia: SIAM, 1974. · Zbl 0291.41020
[14] Singer, I.: Some classes of non-linear operators generalizing the metric projections onto ?eby?ev subspaces. In: Proc. Fifth Internat. Summer School ?Theory of Nonlinear Operators?, held in Berlin 1977. Abhandl. Akad. Wiss. DDR, Abt. Math.-Naturwiss.-Technik 6 N. 245-257 (1978).
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