Geodesic
Exact estimates of approximation by abstract Kantorovich type operators in terms of the second modulus of continuity
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 48, Tome 491 (2020), pp. 66-93 Cet article a éte moissonné depuis la source Math-Net.Ru

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Approximation of bounded measurable functions on the segment $[0, 1]$ by Kantorovich type operators $$ B_n(f)(x)=\sum_{j=0}^nC_n^jx^j(1-x)^{n-j}F_{j}(f), $$ where $F_{j}$ are functionals possessing sufficiently small supports and having some symmetry is considered. The error of approximation is estimated in terms of the second modulus of continuity. The result is sharp. 
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     author = {L. N. Ikhsanov},
     title = {Exact estimates of approximation by abstract {Kantorovich} type operators in terms of the second modulus of continuity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_491_a4/}
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L. N. Ikhsanov. Exact estimates of approximation by abstract Kantorovich type operators in terms of the second modulus of continuity. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 48, Tome 491 (2020), pp. 66-93. http://geodesic.mathdoc.fr/item/ZNSL_2020_491_a4/

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[2] L. N. Ikhsanov, “Otsenka priblizheniya operatorami tipa Kantorovicha cherez vtoroi modul nepreryvnosti”, Zap. nauchn. semin. POMI, 480, 2019, 122–147

[3] L. V. Kantorovich, “O nekotorykh razlozheniyakh po polinomam v forme S. N. Bernshteina”, DAN(A), 22 (1930), 595–600

[4] V. S. Videnskii, “Raboty L. V. Kantorovicha o polinomakh N. S. Bernshteina”, Vestnik SPbGU, Ser. 1, 2013, no. 2, 50–53 | Zbl