Geodesic
The best one-sided approximation of one class of functions by another
Matematičeskie zametki, Tome 14 (1973) no. 5, pp. 627-632 
V. G. Doronin; A. A. Ligun. The best one-sided approximation of one class of functions by another. Matematičeskie zametki, Tome 14 (1973) no. 5, pp. 627-632. http://geodesic.mathdoc.fr/item/MZM_1973_14_5_a2/
@article{MZM_1973_14_5_a2,
     author = {V. G. Doronin and A. A. Ligun},
     title = {The best one-sided approximation of one class of functions by another},
     journal = {Matemati\v{c}eskie zametki},
     pages = {627--632},
     year = {1973},
     volume = {14},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_5_a2/}
}
TY  - JOUR
AU  - V. G. Doronin
AU  - A. A. Ligun
TI  - The best one-sided approximation of one class of functions by another
JO  - Matematičeskie zametki
PY  - 1973
SP  - 627
EP  - 632
VL  - 14
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1973_14_5_a2/
LA  - ru
ID  - MZM_1973_14_5_a2
ER  - 
%0 Journal Article
%A V. G. Doronin
%A A. A. Ligun
%T The best one-sided approximation of one class of functions by another
%J Matematičeskie zametki
%D 1973
%P 627-632
%V 14
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1973_14_5_a2/
%G ru
%F MZM_1973_14_5_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

We concern ourselves with problems of the best one-sided approximation of classes of continuous functions. We obtain estimates of the best one-sided approximation of one class of functions by another, and we find exact values of the upper bounds of the best one-sided approximations on the classes $H_\omega$ of $2\pi$-periodic functions [given by an arbitrary convex modulus of continuity $\omega(t)$] by trigonometric polynomials of order not higher than $n-1$ in the $L_{2\pi}$ metric.