On the order of simultaneous approximation of bivariate functions by Bernstein operators

Authors

  • Ion Badea University of Craiova, Romania
  • Cătălin Badea University of Craiova, Romania

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References

Badea, I., Approximation of vector functions of one and two variables by Bernstein polynomials (in Romanian), Doctoral thesis, Univeristy of Craiova, 1974.

Badea, Ion The modulus of oscillation for functions of two variables, and some applications to approximation by Bernšteĭn operators. (Romanian) An. Univ. Craiova Ser. a V-a no. 2, pp. 43-54. (1974), MR0410177.

Badea, Ion, A theorem of Popoviciu on the approximation of functions by means of the Bernstein operators. (Romanian. French summary) Bul. Ştiinţ. Inst. Politehn. Cluj-Napoca Ser. Electrotehn.-Energet.-Inform. 25 (1982), pp. 7-10, MR0784106.

Badea, I. and Badea, C., On an inequality of Sikkema concerning the approximation with Bernstein operator (submitted for publication).

Gonska, Heinz H. Quantitative Korovkin type theorems on simultaneous approximation. Math. Z. 186 (1984), no. 3, pp. 419-433, MR0744832, https://doi.org/10.1007/bf01174895

Ipatov, A. F. Estimation of the error and order of approximation of functions of two variables by Bernstein polynomials. (Russian) Uč. Zap. Petrozavodsk. Gos. Univ. 4 1955 no. 4, pp. 31-48 (1957),MR0125378.

Kingsley, Edward H. Bernstein polynomials for functions of two variables of class C(k). Proc. Amer. Math. Soc. 2, (1951), pp. 64-71, MR0042548, https://doi.org/10.1090/s0002-9939-1951-0042548-7

Knoop, Hans-Bernd; Pottinger, Peter, Ein Satz vom Korovkin-Typ für Ck-Räume. (German) Math. Z. 148 (1976), no. 1, pp. 23-32, MR0415168, https://doi.org/10.1007/bf01187866

Moldovan, Grigor On the approximation of continuous functions by Bernstein polynomials. (Romanian) Studia Univ. Babecedla s-Bolyai Ser. Math.-Phys. 11 1966 no. 1, pp. 63-71, MR0203313.

Moldovan, Gr., L'évaluation de l'erreur de l'approximation d'une fonction continue par certains opérateurs linéaires positifs. (French) Mathematica (Cluj) 22(45) (1980), no. 1, pp. 85-95, MR0618033.

Moldovan, Grigor; Rîp, Ilie On an inequality in the theory of approximation of functions of two variables by Bernstein polynomials. (Romanian) Stud. Cerc. Mat. 18 1966, pp. 845-853, MR0213792.

Schurer, F., On the order of approximation with generalized Bernstein polynomials. Nederl. Akad. Wetensch. Proc. Ser. A 65 = Indag. Math. 24 1962 484-488, MR0141922, https://doi.org/10.1016/s1385-7258(62)50046-2

Sikkema, P. C., Der Wert einiger Konstanten in der Theorie der Approximation mit Bernstein-Polynomen. (German) Numer. Math. 3 1961, pp. 107-116, MR0123128, https://doi.org/10.1007/bf01386008

Stancu, D. D. Sur l'approximation des dérivées des fonctions par les dérivées correspondantes de certaines polynomes du type Bernstein. (French) Mathematica (Cluj) 2 (25) 1960, pp. 335-348, MR0130516.

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Published

1987-02-01

How to Cite

Badea, I., & Badea, C. (1987). On the order of simultaneous approximation of bivariate functions by Bernstein operators. Anal. Numér. Théor. Approx., 16(1), 11–17. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1987-vol16-no1-art2

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