Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 457-468
Citer cet article
R. K. Vasil'ev. On the order of an approximation of functions on sets of positive measure by linear positive polynomial operators. Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 457-468. http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a16/
@article{MZM_1973_13_3_a16,
author = {R. K. Vasil'ev},
title = {On the order of an~approximation of functions on sets of positive measure by linear positive polynomial operators},
journal = {Matemati\v{c}eskie zametki},
pages = {457--468},
year = {1973},
volume = {13},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a16/}
}
TY - JOUR
AU - R. K. Vasil'ev
TI - On the order of an approximation of functions on sets of positive measure by linear positive polynomial operators
JO - Matematičeskie zametki
PY - 1973
SP - 457
EP - 468
VL - 13
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a16/
LA - ru
ID - MZM_1973_13_3_a16
ER -
%0 Journal Article
%A R. K. Vasil'ev
%T On the order of an approximation of functions on sets of positive measure by linear positive polynomial operators
%J Matematičeskie zametki
%D 1973
%P 457-468
%V 13
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a16/
%G ru
%F MZM_1973_13_3_a16
It is proved that at almost all points the order of approximation, even of one of the functions 1, $\cos x$, $\sin x$ by means of a sequence of linear positive polynomial operators having uniformly bounded norms, is not higher than $1/n^2$. Refinements of this result are given for operators of convolution type.
