Approximation properties of a bivariate Stancu type operator

Authors

  • Dan Bărbosu North University of Baia Mare, Romania

DOI:

https://doi.org/10.33993/jnaat341-787

Keywords:

Stancu's operators, Korovkin theorem, bivariate function, modulus of smoothness, Voronovskaia theorem
Abstract views: 205

Abstract

An extension of Stancu's operator \(P_{m}^{(\alpha ,\beta )}\) to the case of bivariate functions is presented and some approximation properties of this operator are discussed.

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References

Altomore, F., Campiti, M., Korovkin-type Approximation Theory and its Application, de Gruyter Series Studies in Mathematics, 17, Walter de Gruyter &Co, Berlin, New-York, 1994.

Badea, C., Badea, I., Gonska, H.H., A test function theorem and approximation by pseudopolynomials, Bull. Austral. Math. Soc., 34, pp. 53-64, 1986, https://doi.org/10.1017/s0004972700004494 DOI: https://doi.org/10.1017/S0004972700004494

Badea, C., Cottin., Korovkin-type theorems for Generalided Boolean Sum Operators, Colloguia Mathematica Societatis Janos Bolyai, 58, Approximation Theory, Kecskemet (Hungary), 51-68, 1990.

Barbosu, D., A Voronovskaia-type theorem for the bivariate operator of Stancu (submitted).

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Bőgel, K., Ubër die mehrdimensionale Differentiation Integration und beschrankte Variation, J. Reine Angew. Math., 173, pp. 5-29, 1935. DOI: https://doi.org/10.1515/crll.1935.173.5

Dobrescu, E., Matei, I., Aproximarea prin polinoame de tip Bernstein a funcţiilor bidimensional continue, Anal. Univ. Timişoara, Seria Ştiinţe matematice fizice, IV, pp. 85-90, 1966.

Stancu, D.D., Approximation of functions by a new class of linear polynomial operators, Rev. Roum. Math. Pures et Appl., 13, no. 8, pp. 1173-1194, 1968.

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Stancu, F., Aproximarea funcţiilor de două şi mai multe variabile cu ajutorul operatorilor liniari pozitivi, Ph. D. Thesis, Cluj-Napoca, 1984 (in Romanian).

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Published

2005-02-01

How to Cite

Bărbosu, D. (2005). Approximation properties of a bivariate Stancu type operator. Rev. Anal. Numér. Théor. Approx., 34(1), 17–21. https://doi.org/10.33993/jnaat341-787

Issue

Vol. 34 No. 1 (2005)

Section

Articles

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

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