A survey on recent results in Korovkin’s approximation theory in modular spaces

In this paper we give a survey about recent versions of Korovkin-type theorems for modular function spaces, a class which includes Lp, Orlicz and Musielak-Orlicz spaces, with respect to various kinds of convergence, like triangular matrix statistical convergence and filter convergence (which are generalizations of the statistical convergence), and an abstract axiomatic convergence which includes the previous ones and even almost convergence, which is not generated by any filter.