Matematičeskie zametki, Tome 10 (1971) no. 5, pp. 571-582
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V. È. Gheit. On the exactness of certain inequalities in approximation theory. Matematičeskie zametki, Tome 10 (1971) no. 5, pp. 571-582. http://geodesic.mathdoc.fr/item/MZM_1971_10_5_a12/
@article{MZM_1971_10_5_a12,
author = {V. \`E. Gheit},
title = {On the exactness of certain inequalities in approximation theory},
journal = {Matemati\v{c}eskie zametki},
pages = {571--582},
year = {1971},
volume = {10},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_5_a12/}
}
TY - JOUR
AU - V. È. Gheit
TI - On the exactness of certain inequalities in approximation theory
JO - Matematičeskie zametki
PY - 1971
SP - 571
EP - 582
VL - 10
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1971_10_5_a12/
LA - ru
ID - MZM_1971_10_5_a12
ER -
%0 Journal Article
%A V. È. Gheit
%T On the exactness of certain inequalities in approximation theory
%J Matematičeskie zametki
%D 1971
%P 571-582
%V 10
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1971_10_5_a12/
%G ru
%F MZM_1971_10_5_a12
We prove the following: for every sequence $\{F_\nu\}$, $F_\nu\downarrow0$, $F_\nu>0$ there exists a function $\begin{array}{l} 1)~E_n(f)\leqslant F_n\quad(n=0,1,2,\dots) \text{ и }\\ 2)~A_kn^{-k}\sum_{\nu=1}^n\nu^{k-1}F_{\nu-1}\leqslant\omega_k(f,n^{-1})\quad(n=1,2,\dots). \end{array}$
