The approximation of bivariate functions by bivariate operators and GBS operators

Authors

  • Ovidiu T. Pop National College "Mihai Eminescu", Satu Mare, Romania

DOI:

https://doi.org/10.33993/jnaat401-952

Keywords:

linear positive operators, bivariate operators, GBS operators, Voronovskaja-type theorem, approximation theorem, generalized boolean sum operator
Abstract views: 235

Abstract

In this paper we demonstrate a general approximation theorem for the bivariate functions by bivariate operators and GBS (Generalized Boolean Sum) operators.

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References

Badea, C. and Cottin, C., Korovkin-type Theorems for Generalized Boolean Sum Operators, Colloquia Mathematica Societatis János Bolyai, 58, Approximation Theory, Kecskemét (Hungary), pp. 51-67, 1990.

Pop, O. T., The generalization of Voronovskaja's theorem for a class of linear and positive operators, Rev. Anal. Num. Théor. Approx., 34, No. 1, pp. 79-91, 2005.

Pop, O. T., About some linear and positive operators defined by infinite sum, Dem. Math., XXXIX, No. 2, pp. 377-388, 2006.https://doi.org/10.1515/dema-2006-0216 DOI: https://doi.org/10.1515/dema-2006-0216

Pop, O. T., About operator of Bleimann, Butzer and Hahn, Anal. Univ. Timişoara, XLIII, Fasc. 1, pp. 117-127, 2005.

Pop, O. T., The generalization of Voronovskaja's theorem for a class of bivariate operators, anal. Univ. Oradea, Fasc. Matematica, Tom XV, pp. 155-169, 2008.

Pop, O. T., About a general property for a class of linear positive operators and applications, Rev. Anal. Num. Théor. Approx., 34, No. 2, pp.175-180, 2005.

Pop, O. T., The generalization of Voronovskaja's theorem for a class of bivariate operators defined by infinite sum, Studia Univ. "Babeş-Bolyai", Mathematica LIII, No. 2, pp.85-107, 2008.

Pop, O. T., Voronovskaja-type theorems and approximation theorems for a class of GBS operators, Fasc. Math., 42, pp. 91-108, 2009.

Pop, O. T., Voronovskaja-type theorem for certain GBS operators, Glasnik Matematički, 43 (63), pp. 179-194, 2008 https://doi.org/10.3336/gm.43.1.12. DOI: https://doi.org/10.3336/gm.43.1.12

Stancu, D. D., Coman, Gh., Agratini, O. and Trîmbiţaş, R., Analiză numerică şi teoria aproximării, I, Presa Universitară Clujeană, Cluj-Napoca, 2001 (in Romanian).

Timan, A. F., Theory of Approximation of Functions of Real Variable, New York: Macmillan Co. 1963, MR22#8257. DOI: https://doi.org/10.1016/B978-0-08-009929-3.50008-7

Voronovskaja, E., Détermination de la forme asymptotique d'approximation des fonctions par les polynômes de M. Bernstein, C. R. Acad. Sci. URSS, pp. 79-85, 1932.

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Published

2011-02-01

How to Cite

Pop, O. T. (2011). The approximation of bivariate functions by bivariate operators and GBS operators. Rev. Anal. Numér. Théor. Approx., 40(1), 64–79. https://doi.org/10.33993/jnaat401-952

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