On uniformly continuous almost best generalized rational approximation operators
type: Item
instance of: scholarly article
title: On uniformly continuous almost best generalized rational approximation operators
zbMATH Open document ID: 1208.41015
DOI: 10.1134/S0001434610010207
author: K. S. Ryutin
published in: Mathematical Notes
publication date: 2010-09-24T00:00:00Z
review text: For finite-dimensional subspaces \(V\) and \(W\) of \(C(K)\) -- for a compact metric space \(K\) -- let \(R(V/W)\) be the closure in \(C(K)\) of \[ \{v/w : v\in V,\;w\in W \text{ and } w > 0 \text{ on } K\}. \] This work identifies the conditions under which, for \(\varepsilon > 0\), there is a continuous (or uniformly continuous) mapping \(P(f)\) of \(C(K)\) into \(R(V/W)\) such that \[ \| f- P(f)\| < (1+\varepsilon) \text{dist}(f, R(V/W)). \]
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 5791032
zbMATH Keywords: near best approximation
reviewed by: Daniel Wulbert
MaRDI profile type: Publication
cites work: On the rational Tschebyscheff operator
description: scientific article; zbMATH DE number 5791032