Geodesic
The exact Jackson--Stechkin inequality in $L_{2,\mu_{\alpha}}$
Čebyševskij sbornik, Tome 24 (2023) no. 3, pp. 139-161

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Several extremal problems on the best mean-square approximation of the functions $f,$ on a semiaxis with a power-law weight are solved in the paper, which can be applied in solving various problems. Exact Jackson–Stechkin-type inequalities are obtained for some classes of functions in which the values of the best approximations are estimated from above in terms of $k$-th order Hankel moduli of smoothness.
Keywords: Jackson inequality, moduli of smoothness, best approximation, exact constants. 
@article{CHEB_2023_24_3_a7,
     author = {T. E. Tileubayev},
     title = {The exact {Jackson--Stechkin} inequality in $L_{2,\mu_{\alpha}}$},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {139--161},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2023_24_3_a7/}
}
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T. E. Tileubayev. The exact Jackson--Stechkin inequality in $L_{2,\mu_{\alpha}}$. Čebyševskij sbornik, Tome 24 (2023) no. 3, pp. 139-161. http://geodesic.mathdoc.fr/item/CHEB_2023_24_3_a7/