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
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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.
@article{ZNSL_2020_491_a4,
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},
pages = {66--93},
publisher = {mathdoc},
volume = {491},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_491_a4/}
}
TY - JOUR AU - L. N. Ikhsanov TI - Exact estimates of approximation by abstract Kantorovich type operators in terms of the second modulus of continuity JO - Zapiski Nauchnykh Seminarov POMI PY - 2020 SP - 66 EP - 93 VL - 491 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2020_491_a4/ LA - ru ID - ZNSL_2020_491_a4 ER -
%0 Journal Article %A L. N. Ikhsanov %T Exact estimates of approximation by abstract Kantorovich type operators in terms of the second modulus of continuity %J Zapiski Nauchnykh Seminarov POMI %D 2020 %P 66-93 %V 491 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2020_491_a4/ %G ru %F ZNSL_2020_491_a4
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/