Monotone and comonotone polynomial approximation revisited
type: Item
instance of: scholarly article
title: Monotone and comonotone polynomial approximation revisited
zbMATH Open document ID: 0697.41001
DOI: 10.1016/0021-9045(88)90071-8
published in: Journal of Approximation Theory
publication date: 1988-01-01T00:00:00Z
review text: Let the \(L_ p[-1,1]\) best approximation by nth degree monotone polynomials to a monotone function f be denoted by \(E^*_ n(f)_ p\). The author proves \(E^*_ n(f)_ p\leq C\omega^ 2_{\phi}(f,1/n)_ p,\) where \(\phi (x)=\sqrt{1-x^ 2}\) and \(\omega^ 2_{\phi}(f,t)_ p=\sup_{0<h\leq t}\| \Delta^ 2_{h\phi}f\|_{L_ p[-1,1]}.\) The result was proved for polynomial approximation by \textit{V. Totik} and the reviewer in ``Moduli of smoothness'' (1987; Zbl 0666.41001). Using Theorem 3.1.2 of the book, one observes that the result of \textit{Xianming Yu} [Acta Math. Sin., New Ser. 3, 315-326 (1987; Zbl 0637.41004)] and the present result are equivalent. The proof in the present paper is, however, somewhat clearer.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 4142708
author: D. Leviatan
MaRDI profile type: Publication
full work available at URL: 0021-9045(88)90071-8
OpenAlex ID: W2055674814
cites work: On Comonotone Approximation
cites work: Monotone Approximation by Polynomials
cites work: Pointwise estimates for monotone polynomial approximation
cites work: On interpolation of L//p[a,b] and weighted Sobolev spaces
cites work: Polynomials of best approximation in C[-1,1]
cites work: Q3817079
cites work: Exact estimates for partially monotone approximation
cites work: The Degree of Copositive Approximation by Polynomials
cites work: Q4049510
cites work: Degree of approximation by monotone polynomials. I
cites work: Efficient co-monotone approximation
description: scientific article; zbMATH DE number 4142708