Geodesic
Multidimensional approximation operators generated by Lebesgue--Stieltjes measures
Izvestiya. Mathematics , Tome 22 (1984) no. 3, pp. 399-418.

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A general class of sequences of multidimensional positive linear operators is defined and studied; it includes, in particular, sequences of multidimensional Berstein polynomials. The main asymptotic term is obtained in the remainder when derivatives of functions in certain classes are approximated by derivatives of the values of the operators on these functions. Bibliography: 10 titles. 
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Yu. I. Volkov. Multidimensional approximation operators generated by Lebesgue--Stieltjes measures. Izvestiya. Mathematics , Tome 22 (1984) no. 3, pp. 399-418. http://geodesic.mathdoc.fr/item/IM2_1984_22_3_a0/

[1] Nikolskii S. M., “Priblizhenie mnogochlenami funktsii deistvitelnogo peremennogo”, Matematika v SSSR za 30 let, Gostekhizdat, M., L., 1948

[2] Esseen C. G., “Über die asymtotisch beste Approximation steitiger Funktionen mit Hilf von Bernstein-Polinomen”, Numer. Math., 2:4 (1960), 206–213 | DOI | MR | Zbl

[3] Rathore R. K. S., “Lipschtz–Nikolskii Constants for the Gamma Operators of Muller”, Math. Z., 141:2 (1975), 193–198 | DOI | MR | Zbl

[4] Holzle G. E., “On the degree of approximation of continuous funktions by a class of sequences of linear positive operators”, Proz. Kon. Ned. Akad. Wetensch., A83:2 (1980), 171–181 | MR

[5] V. S. Korolyuk (red.), Spravochnik po teorii veroyatnostei i matematicheskoi statistike, Naukova dumka, Kiev, 1978 | MR

[6] Beitmen G. i Erdeii A., Vysshie transtsendentnye funktsii: funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonalnye mnogochleny, Nauka, M., 1966 | MR

[7] Billingsli P., Skhodimost veroyatnostnykh mer, Nauka, M., 1977 | MR

[8] Korovkin P. P., Lineinye operatory i teoriya priblizhenii, Fizmatgiz, M., 1959

[9] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. 2, Mir, M., 1967

[10] Volkov Yu. I., “O nekotorykh lineinykh polozhitelnykh operatorakh”, Matem. zametki, 23:5 (1978), 659–669 | MR | Zbl