Multidimensional analogues of direct and converse Jackson and Bernshtein theorems and their generalizations
Matematičeskie zametki, Tome 67 (2000) no. 4, pp. 608-615.

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A. Khatamov. Multidimensional analogues of direct and converse Jackson and Bernshtein theorems and their generalizations. Matematičeskie zametki, Tome 67 (2000) no. 4, pp. 608-615. http://geodesic.mathdoc.fr/item/MZM_2000_67_4_a14/

[1] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969

[2] Berg I., Lefstrem I., Interpolyatsionnye prostranstva. Vvedenie, Mir, M., 1980

[3] Jackson D., Über die Genauigkeit der Annaherung stetiger Funktion durch ganze rationale Funktionen gegebenen Grades und trigonometrische Summen gegebener Ordnung, Dis., Gottingen, 1911

[4] Bernshtein S. N., Sobr. soch., T. 1, Izd-vo AN SSSR, M., 1952, 11–104

[5] Valloe Poussin Ch. J., De la Lecons sur l'approximation desfunctions d'une variable reelle, Gauthier-Villars, Paris, 1919

[6] Daugavet I. K., Vvedenie v teoriyu priblizheniya funktsii, Izd-vo Leningradskogo un-ta, L., 1977 | Zbl

[7] Nikolskii S. M., “Nekotorye voprosy priblizheniya funktsii mnogikh peremennykh”, Konstruk. teor. f-i, Tr. Mezhdunar. konf. (Varna, 1970), Izd-vo BAN, Sofiya, 1972, 81–83

[8] Konovalov V. N., “Priblizhenie mnogochlenami funktsii mnogikh peremennykh s sokhraneniem differentsialno-raznostnykh svoistv”, Ukr. matem. zh., 36:2 (1984), 154–159 | MR

[9] Brudnyi Yu. A., “Ob odnoi approksimatsionnoi lemme i ee primeneniyakh”, Teoriya funk. an. i ikh prilozh., 1972, no. 15, 180–189 | MR | Zbl

[10] Brudnyi Yu. A., “Teorema prodolzheniya dlya odnogo semeistva funktsionalnykh prostranstv”, Zapiski nauch. sem. LOMI, 56, Nauka, L., 1976, 170–173 | MR | Zbl

[11] Nikolskii S. M., “Ob odnom metode pokrytiya oblasti i neravenstva dlya mnogochlenov ot mnogikh peremennykh”, Mathematica, 8 (1966), 345–356 | MR | Zbl

[12] Khatamov A., “Pryamye i obratnye teoremy teorii polinomialnykh approksimatsii funktsii mnogikh peremennykh”, Uzb. matem. zh., 1993, no. 4, 66–76

[13] Ivanov K. G., “Approximation of a convex function by means of polinomials and polygons in $L$-metric”, Approximation and function spaces, Proc. Conf. (Gdansk, 1979), 287–293

[14] Stojanova M. P., “Approximation of a convex function by algebraic polinomials in $L_p[a,b]$ ($1

\infty $)”, Serdica bulg. math. publ., 11 (1985), 392–397 | MR | Zbl