Geodesic
The best one-sided approximation of the classes $W^rH_\omega$
Matematičeskie zametki, Tome 21 (1977) no. 3, pp. 313-327.

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In this paper we calculate the upper bounds of the best one-sided approximations, by trigonometric polynomials and splines of minimal defect in the metric of the space $L$, of the classes $W^rH_\omega$ ($r=2,4,6,\dots$) of all $2\pi$-periodic functions $f(x)$ that are continuous together with their $r$-th derivative $f^r(x)$ and such that for any points $x'$ and $x''$ we have $|f^r(x')-f^r(x'')|\le\omega(|x'-x''|)$, where $\omega(t)$ is a modulus of continuity that is convex upwards. 
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     author = {V. G. Doronin and A. A. Ligun},
     title = {The best one-sided approximation of the classes $W^rH_\omega$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {313--327},
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     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_3_a3/}
}
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V. G. Doronin; A. A. Ligun. The best one-sided approximation of the classes $W^rH_\omega$. Matematičeskie zametki, Tome 21 (1977) no. 3, pp. 313-327. http://geodesic.mathdoc.fr/item/MZM_1977_21_3_a3/