Approximation results with respect to multidimensional \(\varphi \)-variation for nonlinear integral operators
type: Item
instance of: scholarly article
title: Approximation results with respect to multidimensional \(\varphi \)-variation for nonlinear integral operators
zbMATH Open document ID: 1263.26023
DOI: 10.4171/ZAA/1476
author: Laura Angeloni
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2013-03-11T00:00:00Z
review text: Summary: We study approximation problems for functions belonging to \(BV\varphi \)-spaces (spaces of functions of bounded \(\varphi \)-variation) in a multidimensional setting. In particular, using a multidimensional concept of \(\varphi \)-variation in the sense of Tonelli introduced in [the author and \textit{G. Vinti}, J. Math. Anal. Appl. 349, No. 2, 317--334 (2009; Zbl 1154.26017)], we obtain estimates, convergence results and, by means of suitable Lipschitz classes, results about the order of approximation for a family of nonlinear convolution integral operators.
Mathematics Subject Classification ID: 26B30
Mathematics Subject Classification ID: 26A45
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A35
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 6143108
zbMATH Keywords: nonlinear convolution integral operators
zbMATH Keywords: multidimensional \(\varphi \)-variation
zbMATH Keywords: rate of approximation
zbMATH Keywords: Lipschitz classes
zbMATH Keywords: \(\varphi \)-modulus of smoothness
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/1476
OpenAlex ID: W2039622009
description: scientific article; zbMATH DE number 6143108