Geodesic
Exact constants in Jackson--Stechkin inequality in $L^{2}$ with a power-law weight
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 1, pp. 259-279

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In this paper, we have solved several extremal problems of the best mean-square approximation of function $f$, on the semiaxis with a power-law weight, which can be used to solve various problems. Sharp Jackson–Stechkin type inequalities are obtained on some classes of functions in which the values of the best approximations are estimated from above through moduli of smoothness of the $k$-th order.
Keywords: exact constants in Jackson–Stechkin inequality, moduli of smoothness, best approximations, Bessel function. 
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     author = {T. E. Tileubayev},
     title = {Exact constants in {Jackson--Stechkin} inequality in $L^{2}$ with a power-law weight},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2023_29_1_a19/}
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T. E. Tileubayev. Exact constants in Jackson--Stechkin inequality in $L^{2}$ with a power-law weight. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 1, pp. 259-279. http://geodesic.mathdoc.fr/item/TIMM_2023_29_1_a19/