zbMATH — the first resource for mathematics

Bernstein-Durrmeyer type operators. (English) Zbl 1114.41012
Summary: We introduce modified Bernstein-Durrmeyer operators and study approximation properties of these operators, including theorems on the degree of approximation.

41A35 Approximation by operators (in particular, by integral operators)
Full Text: EuDML
[1] S. N. Bernstein: Demonstration du théoreme de Weierstrass fondée sur la calcul des probabilités. Comm. Soc. Math. Charkow Ser. 2 13 (1912), 1-2.
[2] S. N. Bernstein: Complément a l’article de E. Voronowskaja. Dokl. Akad. Nauk USSR 4 (1932), 86-92. · JFM 58.1062.05
[3] M. M. Derriennic: Sur l’approximation de fonctions integrable sur [0,1] par des polynomes de Bernstein modifiés. J. Approx. Theory 31 (1981), 325-343. · Zbl 0475.41025 · doi:10.1016/0021-9045(81)90101-5
[4] R. A. De Vore G. G. Lorentz: Constructive Approximation. Springer-Verlag, Berlin, 1993. · Zbl 0797.41016
[5] Z. Ditzian K. G. Ivanov: Bernstein-type operators and their derivatives. J. Approx. Theory, 56 (1989), 72-90. · Zbl 0692.41021 · doi:10.1016/0021-9045(89)90134-2
[6] J. L. Durrmeyer: Une formule d’inversion de la transformée de Laplace: Applications a la théorie des moments. These de 3e cycle, Faculte des Sciences de l’Universite de Paris, 1967.
[7] A. Il’inskii S. Ostrovska: Convergence of generalized Bernstein polynomials. J. Approx. Theory 116 (2002), 100-112. · Zbl 0999.41007 · doi:10.1006/jath.2001.3657
[8] G. H. Kirov: A generalization of the Bernstein polynomials. Math. Balkanica 6(2) (1992), 147-153. · Zbl 0838.41017
[9] G. G. Lorentz: Bernstein Polynomials. Chelsea, New York, 1986. · Zbl 0989.41504
[10] V. Videnskii: Bernstein Polynomials. Leningrad State Pedagogical University, Leningrad, 1990. [in Russian] · Zbl 1285.41001
[11] V. Videnskii: New Topics Concerning Approximation by Positive Linear Operators. Open Problems in Approximation Theory, 1993, Bulgaria, pp. 205-212. Editor Borislav Bojanov.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.