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Rozema, Edward R.; Smith, Philip W.

Nonlinear approximation in uniformly smooth Banach spaces. (English) Zbl 0251.41018

Trans. Am. Math. Soc. 188, 199-211 (1974).
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Cited in 2 Documents

MSC:

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

[1] V. I. Averbuh and O. G. Smoljanov, Differentiation theory in linear topological spaces, Uspehi Mat. Nauk 22 (1967), no. 6 (138), 201 – 260 (Russian).
[2] Melvyn Berger and Marion Berger, Perspectives in nonlinearity. An introduction to nonlinear analysis., W. A. Benjamin, Inc., New York-Amsterdam, 1968. · Zbl 0185.22102
[3] Dennis F. Cudia, The geometry of Banach spaces. Smoothness, Trans. Amer. Math. Soc. 110 (1964), 284 – 314. · Zbl 0123.30701
[4] J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. X, Academic Press, New York-London, 1960. · Zbl 0100.04201
[5] I. C. Gohberg and A. S. Markus, Two theorems on the gap between subspaces of a Banach space, Uspehi Mat. Nauk 14 (1959), no. 5 (89), 135 – 140 (Russian). · Zbl 0093.12003
[6] John R. Rice, The approximation of functions. Vol. 2: Nonlinear and multivariate theory, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. · Zbl 0185.30601
[7] Ivan Singer, Cea mai bună aproximare în spaţii vectoriale normate prin elemente din subspaţii vectoriale, Editura Academiei Republicii Socialiste România, Bucharest, 1967 (Romanian).
[8] L. P. Vlasov, Čebyšev sets and some generalizations of them, Mat. Zametki 3 (1968), 59 – 69 (Russian).
[9] D. E. Wulbert, Continuity of metric projections, Trans. Amer. Math. Soc. 134 (1968), 335 – 341. · Zbl 0164.15003
[10] Daniel Wulbert, Uniqueness and differential characterization of approximations from manifolds of functions, Amer. J. Math. 93 (1971), 350 – 366. · Zbl 0227.41009 · doi:10.2307/2373381
[11] Daniel E. Wulbert, Nonlinear approximation with tangential characterization, Amer. J. Math. 93 (1972), 718 – 730. · Zbl 0227.41010 · doi:10.2307/2373467
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