Geodesic
The approximation of functions by algebraic polynomials
Izvestiya. Mathematics, Tome 2 (1968) no. 4, pp. 735-743 
Yu. A. Brudnyi. The approximation of functions by algebraic polynomials. Izvestiya. Mathematics, Tome 2 (1968) no. 4, pp. 735-743. http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a4/
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     author = {Yu. A. Brudnyi},
     title = {The approximation of functions by algebraic polynomials},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we present a new method for approximating functions by algebraic polynomials. Using this method we prove an approximation theorem in the most general situation, taking into account the position of the point in the interval.

[1] Timan A. F., “Usilenie teoremy Dzheksona”, Dokl. AN SSSR, 81:4 (1951), 509–511 | MR | Zbl

[2] Dzyadyk V. K., “O priblizhenii funktsii obyknovennymi mnogochlenami”, Izv. AN SSSR. Ser. matem., 22 (1958), 337–354 | MR

[3] Freud G., “Über die Approximation reeler stetigen Functionen durch gewöhnliche Polynome”, Math. Ann., 137:1 (1959), 17–25 | DOI | MR | Zbl

[4] Brudnyi Yu. A., “Obobschenie odnoi teoremy A. F. Timana”, Dokl. AN SSSR, 148:6 (1963), 1237–1240 | MR | Zbl

[5] Whitney H., “On functions with bounded $n$-th differences”, J. math. pures et appl., 9:36 (1957), 67–95 | MR

[6] Brudnyi Yu. A., “Ob odnoi teoreme teorii lokalnykh priblizhenii”, Uch. zap. Kazansk. un-ta, 124:6 (1964), 43–49 | MR

[7] Timan A. F., Teoriya priblizheniya funktsii, Gostekhizdat, M., 1960

[8] Whitney H., “On bounded functions with bounded $n$-th differences”, Proc. Amer. Math. Soc., 10:3 (1959), 480–481 | DOI | MR | Zbl