Matematičeskie zametki, Tome 5 (1969) no. 1, pp. 31-37
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V. F. Storchai. The deviation of polygonal functions in the $L_p$ metric. Matematičeskie zametki, Tome 5 (1969) no. 1, pp. 31-37. http://geodesic.mathdoc.fr/item/MZM_1969_5_1_a3/
@article{MZM_1969_5_1_a3,
author = {V. F. Storchai},
title = {The deviation of polygonal functions in the $L_p$ metric},
journal = {Matemati\v{c}eskie zametki},
pages = {31--37},
year = {1969},
volume = {5},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_1_a3/}
}
TY - JOUR
AU - V. F. Storchai
TI - The deviation of polygonal functions in the $L_p$ metric
JO - Matematičeskie zametki
PY - 1969
SP - 31
EP - 37
VL - 5
IS - 1
UR - http://geodesic.mathdoc.fr/item/MZM_1969_5_1_a3/
LA - ru
ID - MZM_1969_5_1_a3
ER -
%0 Journal Article
%A V. F. Storchai
%T The deviation of polygonal functions in the $L_p$ metric
%J Matematičeskie zametki
%D 1969
%P 31-37
%V 5
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1969_5_1_a3/
%G ru
%F MZM_1969_5_1_a3
The precise value is given of the upper bound of the deviation in the $L_p$ metric $(1\le p<\infty)$ of a function $f(x)$ in the class $H_\omega$, given by a convex modulus of continuity $\omega(t)$, from its polygonal approximation at the points $x_k=k/n$ ($k=0,1,\dots,n$).
