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

Abstract

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