Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in \(L_{2}\)
type: Item
instance of: scholarly article
title: Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in \(L_{2}\)
zbMATH Open document ID: 1264.41015
DOI: 10.1134/S0037446611060176
published in: Siberian Mathematical Journal
publication date: 2012-02-24T00:00:00Z
review text: The authors find the exact values of the \(n\)-widths for the classes of periodic differentiable functions in \(L_2[0,2\pi]\) satisfying the constraint \[ \int^h_0 t\widetilde\Omega^{1/m}_m(f^{r}; t)\,dt\leq \Phi(h), \] where \(h> 0\), \(m\in\mathbb{N}\), \(r\in\mathbb{Z}_+\), \(\widetilde\Omega_m^{1/m}(f^{r}; t)\) is the generalized \(m\)th-order continuity modulus of the derivative \(f^{(r)}\in L_1[0,2\pi]\), while \(\Phi(t)\) is an arbitrary increasing function such that \(\Phi(0)= 0\).
reviewed by: Francisco Pérez Acosta
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 6009108
zbMATH Keywords: space of square integrable functions
zbMATH Keywords: best approximation
zbMATH Keywords: extremal characteristic
zbMATH Keywords: generalized continuity modulus
zbMATH Keywords: width
author: Mirgand Shabozovich Shabozov
author: Gulzorkhon Amirshoevich Yusupov
MaRDI profile type: Publication
cites work: Best approximation of periodic functions by trigonometric polinomials in \(L_ 2\)
cites work: Inequalities containing best approximations and the modulus of continuity of functions in \(L_2\)
cites work: Q3940262
cites work: The exact constant in the Jackson inequality in \(L^ 2\)
cites work: Exact inequalities of Jackson type for periodic functions in space \(L_ 2\)
cites work: The Jackson-Stechkin inequality in \(L^2\) with trigonometric modulus of continuity
cites work: \(K\)-functionals and exact values of \(n\)-widths of some classes in \(L_2\)
cites work: Widths of classes from \(L_2[0,2\pi]\) and minimization of exact constants in Jackson-type inequalities
cites work: Problems in the approximation of \(2\pi \)-periodic functions by Fourier sums in the space \(L_2 (2\pi)\)
cites work: Exact constants in Jackson-type inequalities and exact values of widths
cites work: Q3001738
cites work: Widths of classes of periodic differentiable functions in the space \(L_{2} [0, 2\pi]\)
cites work: Inequalities between the best approximations and homogenizations of moduli of continuity in the space \(L_{2}\)
cites work: DIRECT AND CONVERSE THEOREMS OF JACKSON TYPE IN $ L^p$ SPACES, $ 0<p<1$
cites work: Q3344608
cites work: A sharp inequality of Jackson-Stechkin type in \(L_{2}\) and the widths of functional classes
full work available at URL: s0037446611060176
OpenAlex ID: W2028224333
description: scientific article; zbMATH DE number 6009108