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Pointwise estimates for an interpolation process of S. N. Bernstein

Part of: Harmonic analysis in one variable

Published online by Cambridge University Press:  09 April 2009

A. K. Varma  and
Xiang Ming Yu
A. K. Varma
Affiliation:
University of FloridaGainesville, Florida 32611, U.S.A.
Xiang Ming Yu
Affiliation:
University of South CarolinaColumbia, South Carolina 29208, U.S.A.
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Abstract

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The main object of this paper is to provide the solution of an open problem raised by Professor Ron DeVore concerning constructing interpolating process Hn [f, x] satisfying the inequality (1.11). Results on simultaneous approximation are also obtained.

Keywords

rate of convergenceinterpolation process

MSC classification

Secondary: 42A15: Trigonometric interpolation
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 2 , October 1991 , pp. 284 - 299
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Brudnyi, Ju. A., ‘Generalizations of a theorem of A. F. Timan’, Soviet Math. Dokl. 4 (1963), 244–247.Google Scholar
[2]Dzyadyk, V. K., ‘A further strengthening of Jackson's theorem on the approximation of a continuous functions by ordinary polynomials’, Dokl. Akad. Nauk 121 (1958), 403–406.Google Scholar
[3]Dzyadyk, V. K., ‘On a constructive characteristic of functions satisfying the Lipschitz condition on a finite segment of the real axis’, Izv. Akad. Nauk, SSR 20 (1956), 623–642.Google Scholar
[4]DeVore, R., ‘Degree of approximation’, Approximation Theory II, edited by Lorentz, , Chui, , Schumaker, , pp. 117–162 (Academic Press, 1976).Google Scholar
[5]DeVore, R., ‘Pointwise approximation by polynomials and splines’, Proceedings of the conference on the constructive function theory, pp.132–141 (Kalouga, Soviet Union, 1977).Google Scholar
[6]Lorentz, G. G., Approximation of Functions, 2nd ed. (Chelsea, NY, 1986).Google Scholar
[7]Yu, X. Ming, ‘Pointwise estimate for algebraic polynomial approximation’, Approx. Theory and Applications, 1 (3) (1985), 109–115.Google Scholar
[8]Varma, A. K. and Mills, T. M., ‘A new proof of Telyakovski's Theorem on approximation of functions’, Studia Sci. Math. Hungar. 14 (1979), 241–256.Google Scholar
[9]Varma, A. K. and Mills, T. M., ‘A new proof of Timan's Approximation theorem’, Israel J. Math. (1974), 39–44.Google Scholar
[10]Nikolskii, S. M., ‘On the best approximation of functions satisfying Lipschitz's conditions by polynomials’, Izv. Akad. Nauk. SSR 77 (1951), 969–972.Google Scholar
[12]Timan, A. F., ‘Strengthening of Jackson's theorem on the best approximation of continuous functions on a fintite segment of the real axis’, Dokl. Akad. Nauk. 78 (1951), 17–20.Google Scholar
[12]Timan, A. F., ‘Strengthening of Jackson's theorem on the best approximation of continuous functions on a finite segment of the real axis’, Doki. Akad. Nauk. 78 (1951), 17–20.Google Scholar
[13]Varma, A. K., ‘A new proof of A. F. Timans Approximation Theorem II’, J. Approx. Theory, 18 (1) (1976), 57–62.CrossRefGoogle Scholar