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.