Geodesic
On the rate of approximation of functions by the Bernstein polynomials
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 162-169 
S. A. Telyakovskii. On the rate of approximation of functions by the Bernstein polynomials. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 162-169. http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a14/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The estimates are refined for the deviations of the Bernstein polynomials from functions at a fixed point and for the remainders in the asymptotic formulas for these deviations for differentiable functions.

[1] Lorentz G. G., Bernstein polynomials, 2nd ed., Chelsea Publ. Comp., New York, 1986, 134 pp. | MR

[2] Voronovskaya E. V., “Opredelenie asimptoticheskogo vida priblizheniya funktsii polinomami S. N. Bernshteina”, Dokl. AN SSSR. Ser. A, 4 (1932), 79–85 | Zbl

[3] Bernstein S., “Complément à l'article de E. Voronovskaya “Détermiation de la forme asymptotique de l'approximation des fonctions par les polynomes de M. S. Bernstein””, Dokl. AN SSSR. Ser. A, 4 (1932), 86–92 | Zbl

[4] Telyakovskii S. A., “O priblizhenii differentsiruemykh funktsii mnogochlenami Bernshteina i mnogochlenami Kantorovicha”, Tr. MIAN, 260, 2008, 289–296 | MR

[5] Dzyadyk V. K., Vvedenie v teoriyu ravnomernogo priblizheniya funktsii polinomami, Nauka, M., 1972, 512 pp.

[6] DeVore R. A., Lorentz G. G., Constructive approximation, Springer-Verlag, Berlin, 1993, 449 | MR

[7] Bari N. K., Stechkin S. B., “Nailuchshie priblizheniya i differentsialnye svoistva dvukh sopryazhennykh funktsii”, Tr. Mosk. mat. o-va, 5, 1956, 483–522 | MR | Zbl