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: 189

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.

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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

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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

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