@article{COMIM_2004_12_1_a8,
author = {Walczak, Zbigniew},
title = {Bernstein-Durrmeyer type operators},
journal = {Communications in Mathematics},
pages = {65--72},
year = {2004},
volume = {12},
number = {1},
mrnumber = {2214675},
zbl = {1114.41012},
language = {en},
url = {http://geodesic.mathdoc.fr/item/COMIM_2004_12_1_a8/}
}
Walczak, Zbigniew. Bernstein-Durrmeyer type operators. Communications in Mathematics, Tome 12 (2004) no. 1, pp. 65-72. http://geodesic.mathdoc.fr/item/COMIM_2004_12_1_a8/
[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.
[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. | DOI | MR
[4] R. A. De Vore G. G. Lorentz: Constructive Approximation. Springer-Verlag, Berlin, 1993. | MR
[5] Z. Ditzian K. G. Ivanov: Bernstein-type operators and their derivatives. J. Approx. Theory, 56 (1989), 72-90. | DOI | MR
[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. | DOI | MR
[8] G. H. Kirov: A generalization of the Bernstein polynomials. Math. Balkanica 6(2) (1992), 147-153. | MR | Zbl
[9] G. G. Lorentz: Bernstein Polynomials. Chelsea, New York, 1986. | MR | Zbl
[10] V. Videnskii: Bernstein Polynomials. Leningrad State Pedagogical University, Leningrad, 1990. [in Russian]
[11] V. Videnskii: New Topics Concerning Approximation by Positive Linear Operators. in: Open Problems in Approximation Theory, 1993, Bulgaria, pp. 205-212. Editor Borislav Bojanov.