Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 47, Tome 480 (2019), pp. 122-147
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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/
@article{ZNSL_2019_480_a8,
author = {L. N. Ikhsanov},
title = {Estimates of approximation by {Kantorovich} type operators in terms of the second modulus of continuity},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {122--147},
year = {2019},
volume = {480},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_480_a8/}
}
TY - JOUR
AU - L. N. Ikhsanov
TI - Estimates of approximation by Kantorovich type operators in terms of the second modulus of continuity
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2019
SP - 122
EP - 147
VL - 480
UR - http://geodesic.mathdoc.fr/item/ZNSL_2019_480_a8/
LA - ru
ID - ZNSL_2019_480_a8
ER -
%0 Journal Article
%A L. N. Ikhsanov
%T Estimates of approximation by Kantorovich type operators in terms of the second modulus of continuity
%J Zapiski Nauchnykh Seminarov POMI
%D 2019
%P 122-147
%V 480
%U http://geodesic.mathdoc.fr/item/ZNSL_2019_480_a8/
%G ru
%F ZNSL_2019_480_a8
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.
