The generalization of Voronovskaja's theorem for a class of linear and positive operators

Authors

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

DOI:

https://doi.org/10.33993/jnaat341-794

Keywords:

Bernstein operators, Bernstein-Schurer operators, Bernstein-Stancu operators, Kantorovich operators, Durrmeyer operators, Voronovskaja's theorem
Abstract views: 228

Abstract

In this paper we generalize Voronovskaja's theorem for a class of linear and positive operators, and then, through particular cases, we obtain statements verified by the Bernstein, Schurer, Stancu, Kantorovich and Durrmeyer operators.

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References

Agratini, O., Aproximare prin operatori liniari, Presa Universitară Clujeană, Cluj-Napoca, 2000.

Bărbosu, D., Voronovskaja Theorem for Bernstein-Schurer operators, Bul. Şt. Univ. Baia Mare, Ser. B, Matematică-Informatică, XVIII, nr. 2, pp. 37-140, 2002.

Bărbosu, D. and Bărbosu, M., Some properties of the fundamental polynomials of Bernstein-Schurer, Bul. Şt. Univ. Baia Mare, Ser. B, Matematică-Informatică, XVIII, nr. 2, pp. 133-136, 2002.

Derriennic, M. M., Sur l'approximation de finctions intégrables sur [0,1] par des polynômes de Bernstein modifiés, J. Approx. Theory, 31, pp. 325-343, 1981, https://doi.org/10.1016/0021-9045(81)90101-5 DOI: https://doi.org/10.1016/0021-9045(81)90101-5

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Pop, O. T., About a class of linear and positive operators (to appear in Proced. of ICAM4).

Schurer, F., Linear positive operators in approximation theory, Math. Inst. Techn., Univ. Delft. Report, 1962.

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

Stancu, D. D., Curs şi culegere de probleme de analiză numerică, I, Univ. "Babeş-Bolyai" Cluj-Napoca, Facultatea de Matematică, Cluj-Napoca, 1977.

Stancu, D. D., Asupra unei generalizări a polinoamelor lui Bernstein, Studia Univ. Babeş-Bolyai, Ser. Math.-Phys., 14, pp. 31-45, 1969.

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

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Published

2005-02-01

How to Cite

Pop, O. T. (2005). The generalization of Voronovskaja’s theorem for a class of linear and positive operators. Rev. Anal. Numér. Théor. Approx., 34(1), 79–91. https://doi.org/10.33993/jnaat341-794

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