Geodesic
Upper bounds of best one-sided approximations of the classes $W^rL_\psi$ in the metric of~$L$
Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 257-268.

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The lowest upper bound is obtained for best one-sided approximations of classes $W^rL_\psi$ ($r=1,2,\dots$) by trigonometric polynomials and splines of minimum deficiency with equidistant knots, in the metric of space $L$, where $W^rL_\psi=\{f:f(x+2\pi)=f(x)$, $f^{(r-1)}(x)$ is absolutely continuous, $\|f^{(r)}\|_{L_\psi}\le1\}$ and $L_\psi$ is an Orlicz space. 
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     author = {V. G. Doronin and A. A. Ligun},
     title = {Upper bounds of best one-sided approximations of the classes $W^rL_\psi$ in the metric of~$L$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {257--268},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a9/}
}
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V. G. Doronin; A. A. Ligun. Upper bounds of best one-sided approximations of the classes $W^rL_\psi$ in the metric of~$L$. Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 257-268. http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a9/