This article is cited in 1 paper

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

M. Sh. Shabozov

Tajik National University, Dushanbe

Abstract: 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.

UDC: 517.5

Received: 10.01.2021
Revised: 02.06.2021

DOI: 10.4213/mzm13005

 English version: Mathematical Notes, 2021, 110:3, 432–439

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