One-sided convergence conditions for Hermite-Fejér interpolation of higher order of Lagrange type
type: Item
instance of: scholarly article
title: One-sided convergence conditions for Hermite-Fejér interpolation of higher order of Lagrange type
zbMATH Open document ID: 0918.41006
DOI: 10.1007/BF03322056
published in: Results in Mathematics
publication date: 1999-08-04T00:00:00Z
review text: A uniform convergence theorem is stated, generalizing a previous result for Lagrange interpolation, \textit{P. Vértesi} [Acta Sci. Math. 45, 419-428 (1983; Zbl 0549.41002)]. Given \(f\in C([-1,1])\) let \(L_{nm}^{(\alpha,\beta)}(f)\) be the Hermite-Fejér interpolation polynomial of higher order of Lagrange type. Let \(m\) be fixed, odd. If \[ \delta(f;t)=\begin{cases} o(| \ln t|^{-1}),&\text{if \(-2/m-1/2<\gamma\leq-1/2\)}\\ o(t^{m(\gamma+1/2)}), &\text{if \(-1/2<\gamma<1/m-1/2,\)} \end{cases} \] and \(|\alpha-\beta|<2/m,\) then \[ \lim_{n\to+\infty}\| L_{nm}^{(\alpha,\beta)}(f)-f\|=0. \]
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1267811
zbMATH Keywords: Hermite-Fejér interpolation of higher order of Lagrange type
zbMATH Keywords: Jacobi abscissas
zbMATH Keywords: one-sided modulus of continuity
zbMATH Keywords: Lagrange interpolation
zbMATH Keywords: Hermite-Fejér interpolation
author: Biancamaria Della Vecchia
author: Giuseppe Mastroianni
author: Péter Vértesi
reviewed by: Eleonora A. Storozhenko
MaRDI profile type: Publication
cites work: Q3141056
cites work: Q3343092
cites work: Замечания ОБ Интерполировании
cites work: Hermite-Fejér interpolations of higher order. I
full work available at URL: https://doi.org/10.1007/bf03322056
OpenAlex ID: W1967232468
description: scientific article; zbMATH DE number 1267811