Uniqueness for monotone reciprocals
type: Item
instance of: scholarly article
title: Uniqueness for monotone reciprocals
zbMATH Open document ID: 0722.41028
DOI: 10.1016/0021-9045(90)90060-4
published in: Journal of Approximation Theory
publication date: 1990-01-01T00:00:00Z
review text: Let X be a closed subset of an interval and let P be a linear subspace of C(X). Let \(R=\{1/p:\) 1/p is monotone increasing on X, \(p>0\) and X,p\(\in P\}\). The author shows that if best approximation by monotone decreasing elements of P is unique, then best approximation by elements of R is also unique. The proof uses techniques developed by the author in Trans. Am. Math. Soc. 136, 151-157 (1969; Zbl 0172.343) and Approximation theory IV, Proc. int. Conf., Tex. A \& M Univ. 1983, 441-444 (1983; Zbl 0541.41027).
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 4190365
zbMATH Keywords: monotone reciprocal
zbMATH Keywords: best uniform approximation
author: Charles B. Dunham
reviewed by: Richard M. Aron
MaRDI profile type: Publication
full work available at URL: 0021-9045(90)90060-4
OpenAlex ID: W2077938239
cites work: Best monotone approximation by reciprocals of polynomials
cites work: Uniform approximation with constraints
cites work: Chebyshev Approximation by Families with the Betweeness Property
cites work: Q3327089
description: scientific article; zbMATH DE number 4190365