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. 
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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/

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