Geodesic
Estimates of approximation by Kantorovich type operators in terms of the second modulus of continuity
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 47, Tome 480 (2019), pp. 122-147 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 $$ B_n=\sum_{j=0}^nC_n^jx^j(1-x)^{n-j}F_{n, j}, $$ where the $F_{n, j}$ are functionals produced by probability measures with sufficiently small supports 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 = {Estimates of approximation by {Kantorovich} type operators in terms of the second modulus of continuity},
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L. N. Ikhsanov. Estimates of approximation by Kantorovich type operators in terms of the second modulus of continuity. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 47, Tome 480 (2019), pp. 122-147. http://geodesic.mathdoc.fr/item/ZNSL_2019_480_a8/

[1] R. Paltanea, Approximation theory using positive linear operators, Birkhauser, Boston, 2004 | MR | Zbl

[2] L. V. Kantorovich, “O nekotorykh razlozheniyakh po polinomam v forme S. N. Bernshteina”, DAN(A), 1930, no. 22, 595–600