Approximation theorem in \(L_{p}\) for a class of operators constructed by wavelets


In this paper we deal with a linear operator of Baskakov-type which has been constructed in [1] by using wavelets. Now, we estimate the order of approximation in \(L_{p}\)-space \(\left( 1<p\leq\infty\right)\) for smooth functions.


Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Baskakov-type operators; order of approximation; wavelets.

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O. Agratini, Approximation theorem in Lp for a class of operators constructed  by wavelets, Studia Univ. ”Babeș-Bolyai”, Mathematica, 41 (1996) no. 4, pp. 11-16.


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Studia Universitatis  “Babes-Bolyai” Mathematica

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[1] O.Agratini, Construciton of Baskakov-type operators by wavelets, Revue d’Analyse Numerique et de Theorie de l’Approximation, tome 26, 1-2, 1997, to appear.
[2] Yu.A. Brudnyi and N. Ya. Krugliak, Interpolation Functors and Interpolation Spaces, vol.I, North-Holland Mathematical Library, 1991.
[3] Charles K.Chui,  An Introduction to Wavelets,  Academic Press, Boston, 1992.
[4] I. Daubechies, Ten Lectures on Wavelets,  CBMS-NSF Series in Appl. Math., 61, SIAM Publ.,Philadelphia, 1992., 1992.
[5] H.H.Gonska and Ding-Xuan Zhou,  Using wavelets for Szasz-type operators,  Revue d’Analyse Num erique et de Theorie de l’Approximation, tome 24, 1-2, 1995, 131-145.
[6] Yyes Meyer, Ondelettes et Operateurs,  vol. I and vol.II, Hermann, Paris, 1990, Also, Y. Meyer and R.R. Coifman, vol. III, 1991.


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