Geodesic
Inequalities between Best Polynomial Approximants and Smoothness Characteristics of Functions in~$L_2$
Matematičeskie zametki, Tome 110 (2021) no. 3, pp. 450-458

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Exact constants in Jackson–Stechkin type inequalities are found for the smoothness characteristics $\Lambda_m (f)$, $ m\in\mathbb N$, determined by averaging the norm of finite differences of $m$th order of functions $ f \in L_2$. A solution is given of the extremal problem of finding the supremum for best joint polynomial approximations of functions and their successive derivatives on some classes of functions from $L_2$ whose averaged norms of finite differences are bounded above by $1$.
Keywords: best approximations, upper bound, smoothness characteristic, finite differences. 
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     author = {M. Sh. Shabozov},
     title = {Inequalities between {Best} {Polynomial} {Approximants} and {Smoothness} {Characteristics} of {Functions} in~$L_2$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {450--458},
     publisher = {mathdoc},
     volume = {110},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_3_a9/}
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M. Sh. Shabozov. Inequalities between Best Polynomial Approximants and Smoothness Characteristics of Functions in~$L_2$. Matematičeskie zametki, Tome 110 (2021) no. 3, pp. 450-458. http://geodesic.mathdoc.fr/item/MZM_2021_110_3_a9/