Comparison of inequalities for the minimax series via Tchebychev polynomials
type: Item
instance of: scholarly article
title: Comparison of inequalities for the minimax series via Tchebychev polynomials
zbMATH Open document ID: 0930.41008
DOI: 10.1016/S0377-0427(98)00166-6
author: Jose Maria Almira
author: Francisco Pérez Acosta
published in: Journal of Computational and Applied Mathematics
publication date: 1999-10-05T00:00:00Z
review text: By usig some properties of the Chebychev polynomials \(\{T_n\}\), the authors compare some expressions (called \((\alpha,\beta)\)-inequalities), of the form: \[ S^{[a,b]}(fg)\leq\alpha\bigl(\|f\|_{\infty,[a,b]}S^{[a,b]}(g)+\|g\|_{\infty,[a,b]}S^{[a,b]}(f)\bigr)+\beta S^{[a,b]}(f)S^{[a,b]}(g)\tag{*} \] where \(\alpha\) and \(\beta\) are real constants and \(S^{[a,b]}(fg)\) stands for the minimax series of a product of two functions \(f\) and \(g\) belonging to the Besov space \(B^1_{\infty,1}[a,b]\) [see \textit{N. Hayek} and \textit{F. Pérez Acosta}, Rev. Acad. Canar. Cienc. 6, No. 1, 119-127 (1994; Zbl 0835.41010); \textit{F. Pérez Acosta}, ibid. 8, No. 1, 113-133 (1996; Zbl 0888.41004)]. For the particular values (3,0) and (2,2), they show that these \((\alpha,\beta)\)-inequalities are valid on all \(B^1_{\infty,1}[a,b]\), and in the case (0,6), (*) holds for the functions in \(B^1_{\infty,1}[a,b]\) having zeros on \([a,b]\).
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 1326377
zbMATH Keywords: inequalities
zbMATH Keywords: Chebychev polynomials
zbMATH Keywords: Banach algebras
zbMATH Keywords: minimax series
reviewed by: Nácere Hayek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1326377