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

Authors

  • Sorin G. Gal University of Oradea, Romania

DOI:

https://doi.org/10.33993/jnaat372-888

Keywords:

complex Bernstein-Kantorovich polynomials, complex Stancu-Kantorovich polynomials, Voronovskaja's theorem, exact orders in simultaneous approximation
Abstract views: 242

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.

Downloads

Download data is not yet available.

References

Bărbosu, D., Kantorovich-Stancu type operators, J. Ineq. Pure Appl. Math., 5, No. 3, Article 53 (electronic), 2004. DOI: https://doi.org/10.18514/MMN.2004.71

Gal, S.G., Shape Preserving Approximation by Real and Complex Polynomials, Birkhauser Publ., Boston, Basel, Berlin, 2008. DOI: https://doi.org/10.1007/978-0-8176-4703-2

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 DOI: 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 DOI: 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 DOI: 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 DOI: 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.

Downloads

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. https://doi.org/10.33993/jnaat372-888

Issue

Section

Articles