Geodesic
On a strong form of asymptotic formulas of Voronovskaya–Bernstein type with pointwise estimate of the remainder term
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 32-59
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A number of general results is established concerning strong form of asymptotic formulas of Voronovskaya–Bernstein type. Several examples of their application to concrete approximation methods are given. 
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M. V. Babushkin; V. V. Zhuk. On a strong form of asymptotic formulas of Voronovskaya–Bernstein type with pointwise estimate of the remainder term. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 32-59. http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a2/

[1] I. P. Natanson, Konstruktivnaya teoriya funktsii, M.–L., 1949

[2] R. A. DeVore, G. G. Lorentz, Constructive approximation, Berlin, 1993 | MR

[3] S. N. Bernshtein, Sobranie sochinenii, v. II, M., 1954

[4] S. A. Telyakovskii, “O skorosti priblizheniya funktsii mnogochlenami Bernshteina”, Tr. IMM UrO RAN, 14, no. 3, 2008, 162–169

[5] H. Gonska, “On the degree of approximation in Voronovskaja's theorem”, Stud. Univ. Babeş-Bolyai Math., 52:3 (2007), 103–115 | MR | Zbl

[6] J. A. Adell, J. Bustamante, J. M. Quesada, “Estimates for the moments of Bernstein polynomials”, J. Math. Anal. Appl., 432 (2015), 114–128 | DOI | MR | Zbl

[7] V. V. Zhuk, “O silnom priblizhenii funktsii posredstvom polozhitelnykh operatorov”, Zap. nauchn. semin. POMI, 440, 2015, 68–80

[8] V. V. Zhuk, M. V. Babushkin, A. A. Pudovkin, “O silnoi forme asimptoticheskikh formul tipa Voronovskoi–Bernshteina”, Problemy mat. analiza, 84, 2016, 89–105 | Zbl

[9] I. K. Daugavet, Vvedenie v klassicheskuyu teoriyu priblizheniya funktsii, S.-Peterburg, 2011

[10] V. V. Zhuk, Strukturnye svoistva funktsii i tochnost approksimatsii, L., 1984

[11] V. S. Videnskii, Mnogochleny Bernshteina, L., 1990

[12] I. P. Natanson, “O priblizhënnom predstavlenii funktsii, udovletvoryayuschikh usloviyu Lipshitsa, s pomoschyu integrala Valle–Pussena”, Dokl. AN SSSR, 54:1 (1946), 11–14