\(L^ p\)-inverse theorems for beta operators
type: Item
instance of: scholarly article
title: \(L^ p\)-inverse theorems for beta operators
zbMATH Open document ID: 0753.41025
DOI: 10.1016/0021-9045(91)90031-5
published in: Journal of Approximation Theory
publication date: 1992-06-26T00:00:00Z
review text: For the global degree of approximation of functions \(f\in L_ p[0,\infty)\), \(1\leq p\leq\infty\), by the method of Beta operators in the \(L_ p\)-metric direct and converse results are proved which can be combined to an equivalence result. The proofs make use of a large number of lemmata, a Bernstein type inequality and the equivalence of the Ditzian-Totik modulus of smoothness with an appropriate \(K\)-functional.
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A27
zbMATH DE Number: 21718
zbMATH Keywords: Beta operators
zbMATH Keywords: Ditzian-Totik modulus of smoothness
zbMATH Keywords: \(K\)-functional
author: Ding-Xuan Zhou
reviewed by: Manfred Wolfgang Müller
MaRDI profile type: Publication
full work available at URL: 0021-9045(91)90031-5
OpenAlex ID: W2021146783
cites work: An elementary proof of the inverse theorem for Bernstein polynomials
cites work: A global approximation theorem for Meyer-König and Zeller operators
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cites work: A global inverse theorem for combinations of Bernstein polynomials
cites work: On interpolation of L//p[a,b] and weighted Sobolev spaces
cites work: Rate of convergence of Bernstein polynomials revisited
cites work: Q4126835
cites work: Bernstein-type operators and their derivatives
cites work: Q3817079
cites work: A characterization of weighted Peetre K-functionals
cites work: The \(L_1\) saturation class of the Kantorovic operator
cites work: The \(L^p\)-saturation of the Bernstein-Kantorovitch polynomials
cites work: An interpolation theorem and its applications to positive operators
cites work: Some properties of a new kind of modulus of smoothness
cites work: Uniform approximation by positive operators on infinite intervals
cites work: Uniform approximation by Szasz-Mirakjan type operators
cites work: Problems and solutions concerning Kantorovich operators
cites work: Approximation properties of beta operators
cites work: On sequence-to-sequence transformations
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description: scientific article; zbMATH DE number 21718