Some inequalities between the best polynomial approximation and averaged finite-difference norms in space $L_2$

M. Sh. Shabozov ; M. A. Abdulkhaminov

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2021), pp. 78-91.

Résumé

Exact constants are found in inequalities type Jackson-Stechkin for smoothness characte-ristics $\Lambda_{m}(f), m \in\mathbb{N} $ determined by averaging the norm in $L_{2}$ of finite differences of the $m$-th order of the functions $f$. For function classes, defined by the smoothness characteristic $\Lambda_{m}(f)$, and the majorant $\Phi $ satisfying a certain condition, calculated the exact values of different $n$-widths.

Détail

Keywords: best approximations, finite differences of the $m$-th order, smoothness characteristic, $n$-widths.

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