Abstract Korovkin-type theorems in the filter setting with respect to relative uniform convergence

Abstract

We prove a Korovkin-type approximation theorem using abstract relative uniform filter convergence of anet of functions with respect to another fixed filter, a particular case of which is that of all neighborhoods of a point,belonging to the domain of the involved functions. We give some examples, in which we show that our results are strictgeneralizations of the classical ones.