On the \(L_{p}\)-saturation of the Ye-Zhou operator

Authors

  • Zoltán Finta “Babes-Bolyai” University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat341-791

Keywords:

Ye-Zhou operator, Kantorovich operator, saturation theorem
Abstract views: 195

Abstract

We solve the saturation problem for a class of Ye-Zhou operator \(T_{n}( f , x ) = P_{n}( x ) A_{n} L_{n}( f )\) with suitable sequence of matrices \(\{ A_{n} \}_{n \geq 1}.\) The solution is based on the saturation theorem for the Kantorovich operator established by V. Maier and S. D. Riemenschneider.

Downloads

Download data is not yet available.

References

DeVore, R. A. and Lorentz, G. G., Constructive Approximation, Springer-Verlag, Berlin Heidelberg New York, 1993. DOI: https://doi.org/10.1007/978-3-662-02888-9

Maier, V., The L₁-saturation class of the Kantorovich operator, J. Approx. Theory, 22, pp. 223-232, 1978, https://doi.org/10.1016/0021-9045(78)90054-0 DOI: https://doi.org/10.1016/0021-9045(78)90054-0

Maier, V., Lp-approximation by Kantorovich operators, Analysis Math., 4, pp. 289-295, 1978, https://doi.org/10.1007/bf02020576 DOI: https://doi.org/10.1007/BF02020576

Riemenschneider, S. D., The Lp-saturation of the Bernstein-Kantorovich polynomials, J. Approx. Theory, 23, pp. 158-162, 1978, https://doi.org/10.1016/0021-9045(78)90102-8 DOI: https://doi.org/10.1016/0021-9045(78)90102-8

Ye, M. D. and Zhou, D. X., A class of operators by means of three-diagonal matrices, J. Approx. Theory, 78, pp. 239-259, 1994, https://doi.org/10.1006/jath.1994.1075 DOI: https://doi.org/10.1006/jath.1994.1075

Zhou, D. X., On smoothness characterized by Bernstein type operators, J. Approx. Theory, 81, pp. 303-315, 1995, https://doi.org/10.1006/jath.1995.1052 DOI: https://doi.org/10.1006/jath.1995.1052

Downloads

Published

2005-02-01

How to Cite

Finta, Z. (2005). On the \(L_{p}\)-saturation of the Ye-Zhou operator. Rev. Anal. Numér. Théor. Approx., 34(1), 55–62. https://doi.org/10.33993/jnaat341-791

Issue

Vol. 34 No. 1 (2005)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.