A unified approach to approximation results with applications to nonlinear sampling theory

A unitary approach for convergence results in Musielak-Orlicz spaces by means of nets of nonlinear integral operators is given. The family of integral operators considered is general enough to obtain, as particular cases, several classical families of nonlinear integral operators, such as the convolution ones, the Mellin convolution integral operators or the generalized sampling series. In particular, convergence theorems in Musielak-Orlicz spaces for the nonlinear version of the generalized sampling series are obtained. Moreover, in the setting of Orlicz spaces, the problem of the rate of approximation is also considered.