On some wavelet type linear operators


In this paper is introduced a general a class \(\left( L_{k}\right)_{k\in\mathbb{Z}}\) of linear positive operators of wavelet type. The construction is based on two sequences of real numbers which verify some certain conditions. We also study some properties of the above operators. The main result consists in establishing a Jackson inequality by using the first modulus of smoothness.


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



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O. Agratini, On some wavelet type linear operators, Proceedings of the International Symposium on Numerical Analysis and Approximation Theory, Cluj-Napoca, May 9-11, 2002, pp. 46-53.


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[1] Anastassiou, G., Qusantitative Approximations, Chapamn ^ Hall/CRC, Boca Raton, London, 2001.
[2] Anastassiou, G. and Yu, X. M., Monotone and probabilistic wavelet approximation,  Stochastic Anal. Appl., 10 (1992), 251-264.
[3] Debanath, L., Wavelet  Transforms and Their Applicaitons, Birkhauser, Boston, Basel, 2002.

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