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2007 Approximation by means of nonlinear integral operators in the space of functions with bounded $\varphi-$variation
Laura Angeloni, Gianluca Vinti
Differential Integral Equations 20(3): 339-360 (2007).

Abstract

We study approximation problems by means of nonlinear convolution integral operators for functions belonging to $BV_{\varphi}$-spaces, i.e., functions with bounded $\varphi$-variation in the sense of Musielak-Orlicz. In particular, we obtain estimates and convergence results with respect to $\varphi$-variation. Introducing suitable Lipschitz classes that take into account the $\varphi$-variational functional, the problem of the rate of approximation is also considered.

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Laura Angeloni. Gianluca Vinti. "Approximation by means of nonlinear integral operators in the space of functions with bounded $\varphi-$variation." Differential Integral Equations 20 (3) 339 - 360, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.26016
MathSciNet: MR2293990

Subjects:
Primary: 26A45
Secondary: 26A46 , 41A25 , 41A35 , 47G10

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 3 • 2007
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