APPROXIMATION BY MEANS OF NONLINEAR INTEGRAL OPERATORS IN THE SPACE OF FUNCTIONS WITH BOUNDED φ-VARIATION

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