Inequalities between Best Polynomial Approximants and Smoothness Characteristics of Functions in~$L_2$

M. Sh. Shabozov

Matematičeskie zametki, Tome 110 (2021) no. 3, pp. 450-458.

Résumé

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 $1$.

Détail

Keywords: best approximations, upper bound, smoothness characteristic, finite differences.

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