Approximation by complex Bernstein-Kantorovich and Stancu-Kantorovich polynomials and their iterates in compact disks

Authors

  • Sorin G. Gal University of Oradea, Romania

Keywords:

complex Bernstein-Kantorovich polynomials, complex Stancu-Kantorovich polynomials, Voronovskaja's theorem, exact orders in simultaneous approximation
Abstract views: 201

Abstract

In this paper, Voronovskaja-type results with quantitative upper estimates and the exact orders in simultaneous approximation by some complex Kantorovich-type polynomials and their iterates in compact disks in \(\mathbb{C}\) are obtained.

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References

Bărbosu, D., Kantorovich-Stancu type operators, J. Ineq. Pure Appl. Math., 5, No. 3, Article 53 (electronic), 2004.

Gal, S.G., Shape Preserving Approximation by Real and Complex Polynomials, Birkhauser Publ., Boston, Basel, Berlin, 2008.

Gal, S.G., Voronovskaja's theorem and iterations for complex Bernstein polynomials in compact disks, Mediterr. J. Math., 5, no. 3, pp. 253-272, 2008, https://doi.org/10.1007/s00009-008-0148-z

Gal, S.G., Approximation by complex Bernstein-Stancu polynomials in compact disks, Results in Math., accepted for publication, https://doi.org/10.1007/s00025-008-0335-z

Gal, S.G., Approximation and geometric properties of some complex Bernstein-Stancu polynomials in compact disks, Rev. Anal. Numér. Théor. Approx. (Cluj), 36, No. 1, pp. 67-77, 2007.

Gal, S.G., Exact orders in simultaneous approximation by complex Bernstein polynomials, J. Concr. Applic. Math., 2009, accepted for publication.

Gal, S.G., Exact orders in simultaneous approximation by complex Bernstein-Stancu polynomials, Rev. Anal. Num er. Théor. Approx. (Cluj), 37, No. 1, 2008, in press, http://ictp.acad.ro/jnaat/journal/article/view/2008-vol37-no1-art5

Kantorovich, L.V., Sur certains developpments suivant les polynômes de la forme de S. Bernstein, I, II, C.R. Acad. Sci. URSS, pp. 563-568, pp. 595-600, 1930.

Lorentz, G.G., Bernstein Polynomials, 2nd edition, Chelsea Publ., New York, 1986.

Nagel, J., Asymptotic properties of powers of Kantorovic operators, J. Approx. Theory, 36, pp. 268-275, 1982, https://doi.org/10.1016/0021-9045(82)90046-6

Nagel, J., Kantorovic operators of second order, Monatsh. Math., 95, pp. 33-44, 1983, https://doi.org/10.1007/bf01301146

Razi, Q., Approximation of a function by Kantorovich type operators, Mat. Vest., 41, pp. 183-192, 1989.

Stancu, D.D., Approximation of functions by a new class of linear polynomial operators, Rev. Roumaine. Math. Pures Appl., 13, pp. 1173-1194, 1968.

Stancu, D.D., On a generalization of Bernstein polynomials (in Romanian), Stud. Univ. "Babeş-Bolyai", ser. Math., 14, No. 2, pp. 31-44, 1969.

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Published

2008-08-01

How to Cite

Gal, S. G. (2008). Approximation by complex Bernstein-Kantorovich and Stancu-Kantorovich polynomials and their iterates in compact disks. Rev. Anal. Numér. Théor. Approx., 37(2), 159–168. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2008-vol37-no2-art8

Issue

Vol. 37 No. 2 (2008)

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Articles

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