Approximation of functions from \(C^ r\) by splines of minimal defect
type: Item
instance of: scholarly article
title: Approximation of functions from \(C^ r\) by splines of minimal defect
zbMATH Open document ID: 0708.41009
DOI: 10.1007/BF01158512
published in: Mathematical Notes
publication date: 1988-01-01T00:00:00Z
review text: The author gives an alternative simple proof of the inequalities for the best approximation in the class \(C^{r,\omega}\) with a periodic modulus of continuity and a Jackson's type inequality for \(C^ r\)-functions in \(L^ p\)-norms. The best approximations are considered with respect to splines of order r and of defect 1. Further, there is proved a theorem on estimates in \(L^ 1(0,x)\) of nonincreasing rearrangement of derivatives of functions by those of the ideal Euler splines and the best approximation inequality for splines of order zero in an arbitrary symmetric space.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 4163449
zbMATH Keywords: Jackson's type inequality
zbMATH Keywords: Euler splines
zbMATH Keywords: best approximation inequality
zbMATH Keywords: symmetric space
author: Valeriĭ I. Ivanov
reviewed by: Miroslav Krbec
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4163449