Abstract
Recently J.R. Rice [1] initiated a geometrical study of non-linear approximations. In what follows below we offer a small contribution to certain analytical aspects of meansquare non-linear approximations. One result is to exhibit a family of non-linear topological subspaces of the space C [a, b] with the mean-square metric which has a local unique best approximation property.
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References
Rice, J.R.: “Nonlinear Approximation”, Approximation of Functions. Elsevier Pub. Co., (1965), 111-133.
Kantorovich, L.V. and G.P. Akilov: Functional Analysis in Normed Linear Spaces. MacMillan, New York, 1964.
Meinardus, G.: Approximation von Funktionen und ihre numerische Behandlung.
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© 1968 Springer Basel AG
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Cheney, E.W., Goldstein, A.A. (1968). A Note on Nonlinear Approximation Theory. In: Collatz, L., Meinardus, G., Unger, H. (eds) Numerische Mathematik Differentialgleichungen Approximationstheorie. Internationale Schriftenreihe zur Numerischen Mathematik / International Series of Numerical Mathematics / Série Internationale D’Analyse Numérique, vol 9. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5881-6_21
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DOI: https://doi.org/10.1007/978-3-0348-5881-6_21
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5882-3
Online ISBN: 978-3-0348-5881-6
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