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: 173

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.

Downloads

Download data is not yet available.

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).

Bőgel, K., Mehrdimensionale Differentiation von Funktionen mehrer Veränderlicher, J. Reine Angew. Math., 170, pp. 197-217, 1934. DOI: https://doi.org/10.1515/crll.1934.170.197

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.

Stancu, D. D., Coman, Gh., Agratini, O., Trâmbiţaş, R., Analiză numerică şi teoria aproximării, vol. I, Presa Universitară Clujeană, 2001 (in Romanian).

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

Downloads

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

Section

Articles