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

Abstract

In this paper we give a survey about recent versions of Korovkin-type theorems for modular function spaces, a class which includes $L^p$, Orlicz, Musielak-Orlicz spaces and many others. We consider various kinds of modular convergence, using certain summability processes, like triangular matrix statistical convergence, and filter convergence (which are generalizations of the statistical convergence). Finally, wwe consider an abstract axiomatic convergence which includes the previous ones and even almost convergence, which is not generated by any filter, as we show by an example.