A duality approach to best uniform convex approximation
type: Item
instance of: scholarly article
title: A duality approach to best uniform convex approximation
zbMATH Open document ID: 0764.41035
DOI: 10.1016/0022-247X(91)90308-M
author: Yuesheng Xu
author: Stanley E. Weinstein
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: Let C[a,b] be the space of continuous functions on [a,b] endowed with the uniform norm.Let K be the set of convex functions defined on [a,b].In this paper a duality theorem that expresses the error of the best approximation by means of the elements of K in terms of the supremum of a linear functional is established and this duality to obtain the bounds for the error of best approximation is also used. A similar duality approach has been used by \textit{V. A. Ubhaya} [J. Approximation Theory 12, 146-159 (1974; Zbl 0288.41019)]\ and by the author [J. Math. Anal. Appl. 152, No. 1, 240-251 (1990; Zbl 0729.41026)] to investigate best monotone approximation and best quasi-convex approximation,respectively.
Mathematics Subject Classification ID: 41A80
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 60982
zbMATH Keywords: error of best approximation
zbMATH Keywords: best monotone approximation
zbMATH Keywords: best quasi- convex approximation
reviewed by: D. Zarnadze
MaRDI profile type: Publication
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full work available at URL: 0022-247x(91)90308-m
OpenAlex ID: W2088512155
description: scientific article; zbMATH DE number 60982