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An application of a fixed point theorem to best approximation. (English) Zbl 0349.41013


MSC:

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

[1] Dotson, W. J., Fixed point theorems for nonexpansive mappings on star-shaped subsets of Banach spaces, J. London Math. Soc., 4, 408-410 (1972) · Zbl 0229.47047
[2] Edelstein, M., An extension of Banach’s contraction principle, (Proc. Amer. Math. Soc., 12 (1961)), 7-10 · Zbl 0096.17101
[3] Meinardus, G., (Approximation of Functions: Theory and Numerical Methods (1967), Springer: Springer New York), 26-27, of that author’s monograph · Zbl 0122.30801
[4] Opial, Z., Weak convergence of the sequence of successive approximations for non-expansive mappings, Bull. Amer. Math. Soc., 73, 591-597 (1967) · Zbl 0179.19902
[5] Subrahmanyam, P. V., Erratum, J. Math. Phys. Sci., 9, 195 (1975)
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