A bivariate extension of the Bernstein polynomials


In this paper it is given an extension to two variables of the Bernstein \(B_{n,r}f\) operators and there are investigated their approximation properties.


Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Bernstein polynomials; approximation.

Paper coordinates

O. Agratini, On simultaneous approximation by Stancu-Bernstein operators, Studia Universitatis Babes-Bolyai Mathematica, 42 (1997) no. 2, pp. 5-8.


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Studia Universitatis Babes-Bolyai Mathematica

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Print ISSN

1843-3855  ??

Online ISSN

ISSN-L 1843-3855  ??

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[1] Agratini, O., On a class of linear approximating operators, Mathematica Balkanica (to appear)
[2] Kirov, G.H., A generalization of the Bernstein polynomials, Mathematica Balkanica, vol. 6(1992), 2, 147-153
[3] Manole, C., Asupra aproximării funcțiilor de două și mai multe variabile prin operatori liniari și pozitivi, Studia Univ. Babeș-Bolyai, Cluj, XXV(1980), 4, 32-38
[4] Schempp, W., Bernstein polynomials in several variables, Constructive theory of functions of several variables (Obsewolfach, 1976), Lecture Notes in Mathematics, no.571, Springer Verlag, Berlin, 1977, 212-219
[5] Stancu, D.D., On the approximation of funcitons of two variables by means of a class of linear operators (Proc. Conference on Constructive Function Theory, Varna, 1971), Publishing House Bulgar, Acad, Sci., Sofia, 1972, 327-336.

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