Extensions to the Jackson-type and Landau-Kolmogorov-type sharp inequalities for derivatives of low order.
type: Item
instance of: scholarly article
title: Extensions to the Jackson-type and Landau-Kolmogorov-type sharp inequalities for derivatives of low order.
zbMATH Open document ID: 1096.41012
author: O. L. Vinogradov
author: V. V. Zhuk
published in: Vestnik St. Petersburg University. Mathematics
publication date: 2005-06-23T00:00:00Z
review text: The authors generalized the results obtained by \textit{V. V. Zhuk} [Approximation of periodic functions. Leningrad: Izdat. Leningr. Univ. (1982; Zbl 0521.42003)] regarding the sharp Kolmogorov-Jackson and Akhiezer-Krein-Favard-type inequalities. More exactly, for derivatives of low order the above inequalities are strengthened by passing to finer characteristics of the functions that majorize the moduli of continuity. The results are valid for best approximation by means of splines as well as for an arbitrary step of the modulus of continuity. This is the most important contribution of the authors.
reviewed by: Dan Bărbosu
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 2181919
zbMATH Keywords: modulus of continuity
zbMATH Keywords: seminorm
zbMATH Keywords: sharp Jackson inequalities
zbMATH Keywords: sharp Landau-Kolmogorov inequalities
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2181919