## Differential and Integral Equations

### Approximation by means of nonlinear integral operators in the space of functions with bounded $\varphi-$variation

#### 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.

#### Article information

Source
Differential Integral Equations Volume 20, Number 3 (2007), 339-360.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356039506

Mathematical Reviews number (MathSciNet)
MR2293990

Zentralblatt MATH identifier
1212.26016

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

#### Citation

Angeloni, Laura; Vinti, Gianluca. Approximation by means of nonlinear integral operators in the space of functions with bounded $\varphi-$variation. Differential Integral Equations 20 (2007), no. 3, 339--360. https://projecteuclid.org/euclid.die/1356039506.