Some positive results and counterexamples in comonotone approximation
type: Item
instance of: scholarly article
title: Some positive results and counterexamples in comonotone approximation
zbMATH Open document ID: 0870.41016
author: I. O. Shevchuk
author: D. Leviatan
published in: Journal of Approximation Theory
publication date: 1997-06-10T00:00:00Z
review text: Let \(f\) be a continuous function on \([-1,1]\), which changes its monotonicity \(s\) times in the interval. This paper proves the validity of the Jackson-type estimates for the approximation of \(f\) by algebraic polynomials that are comonotone with it involving the Ditzian-Totik modules of continuity and a constant that depends only on \(s\). This paper also shows by counterexamples that in many cases this is not so, even for functions which possess locally absolutely continuous derivatives.
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A29
zbMATH DE Number: 1019190
zbMATH Keywords: comonotone approximation
zbMATH Keywords: Jackson-type theorem
zbMATH Keywords: Ditzian-Totik modules
reviewed by: Yingguang Shi
MaRDI profile type: Publication
full work available at URL: jath.1997.3038
OpenAlex ID: W2064459995
Wikidata QID: Q124826118
cites work: On Comonotone Approximation
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cites work: Q4396599
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cites work: APPROXIMATION OF MONOTONE FUNCTIONS BY MONOTONE POLYNOMIALS
DOI: 10.1006/JATH.1997.3038
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description: scientific article; zbMATH DE number 1019190