Voronovskaja-type theorems for a certain non-positive linear operator

Authors

  • Ion Badea University of Craiova, Romania
  • Dorin Andrica "Babeş-Bolyai" University, Cluj-Napoca, Romania
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References

Badea, Ion The modulus of continuity in the sense of Bögel, and some applications to approximation by a Bernšteĭn operator. (Romanian) Studia Univ. Babeş-Bolyai Ser. Math.-Mech. 18 (1973), no. 2, pp. 69-78, MR0382921.

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, 43-54. (1974), MR0410177.

Badea, I. and Oprea, M., On approximation by Bernstein type polynomials (in Romanian), Bul. Inst. Petrol şi Gaze Ploieşti, 4, pp. 83-86 (1976).

Bögel, Karl, Mehrdimensionale Differentiation von Funktionen mehrerer reeller Veränderlichen. (German) J. Reine Angew. Math. 170 (1934), pp. 197-217, MR1581409, https://doi.org/10.1515/crll.1934.170.197

Bögel, Karl, Über mehrdimensionale Differentiation, Integration und beschränkte Variation. (German) J. Reine Angew. Math. 173 (1935), pp. 5-30, MR1581453, https://doi.org/10.1515/crll.1935.173.5

Bögel, Karl, Über die mehrdimensionale Differentiation. (German) Jber. Deutsch. Math.-Verein. 65 1962/1963 Abt. 1, pp. 45-71, MR0146311.

Gonska, H.H., On approximation in C(X), Drexel University, Department of Mathematics and Computer Science, Technical Report 5-84 (1984); or in Proceed. Int. Conf. on Constructive Theory of Functions, Golden Sands (Varna, Bulgaria), May 27 - June 2, 1984 (to appear).

Natanson, I. P. Constructive function theory. Vol. I. Uniform approximation. Translated from the Russian by Alexis N. Obolensky Frederick Ungar Publishing Co., New York 1964 ix+232 pp., MR0196340.

Schurer, F.; Steutel, F. W. The degree of local approximation of functions in C1[0,1] by Bernstein polynomials. J. Approximation Theory 19 (1977), no. 1, pp. 69-82, MR0437992.

Sikkema, P. C. On some linear positive operators. Nederl. Akad. Wetensch. Proc. Ser. A 73 = Indag. Math. 32 1970, pp. 327-337, MR0270038, https://doi.org/10.1016/s1385-7258(70)80037-3

Voronovskaja, E. W., Détermination de la forme asymptotique d'approximation des fonctions par les polynômes de M. Bernstein, Dokl. Akad. Nauk SSSR 79, pp. 79-85 (1932).

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Published

1986-08-01

How to Cite

Badea, I., & Andrica, D. (1986). Voronovskaja-type theorems for a certain non-positive linear operator. Anal. Numér. Théor. Approx., 15(2), 95–103. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1986-vol15-no2-art1

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Vol. 15 No. 2 (1986)

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