Geodesic
The best one-sided approximation of one class of functions by another
Matematičeskie zametki, Tome 14 (1973) no. 5, pp. 627-632

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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. 
@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},
     publisher = {mathdoc},
     volume = {14},
     number = {5},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_5_a2/}
}
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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/