Rational approximation in uniform and weighted \(L^ 1\) norm
type: Item
instance of: scholarly article
title: Rational approximation in uniform and weighted \(L^ 1\) norm
zbMATH Open document ID: 0816.41015
DOI: 10.1016/0377-0427(94)90061-2
author: Biancamaria Della Vecchia
author: Giuseppe Mastroianni
published in: Journal of Computational and Applied Mathematics
publication date: 1995-02-09T00:00:00Z
review text: The authors give an estimate for the constant of best approximation of functions from a class of functions having non-uniform smoothness behaviour on \([-1,1]\) in the following sense: \(f \in C^ p ([-1,1])\), \(p \geq 1\), \(f \in C^ q ([c,d])\), \(p < q < \infty\), for every closed segment \([c,d]\) in \([-1,1] \backslash \{a\}\), \(| a | \leq 1\), \(\lim_{x \to a, | x | \leq 1} (a-x)^ k\), \(f^{(p+k)} (x)\) is finite for \(k = 1, \dots, q - p\). Furthermore they consider a class of functions having an integrable singularity in \(a \in [-1,1]\) and that in addition belong to \(C^ q ([c,d])\) for every closed segment \([c,d] \subset [-1,1] \backslash \{a\}\). For this class rational approximation in \(L^ 1\)-norm with respect to a weight function having an algebraic singularity in \([-1,1]\) is studied.
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 721013
zbMATH Keywords: Shepard operators
zbMATH Keywords: pointwise simultaneous approximation
reviewed by: Marcel G. de Bruin
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90061-2
OpenAlex ID: W2087462729
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description: scientific article; zbMATH DE number 721013