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

Authors: ANTONIO BOCCUTO, KAMİL DEMİRCİ, SEVDA YILDIZ

Abstract: We prove a Korovkin-type approximation theorem using abstract relative uniform filter convergence of a net 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 strict generalizations of the classical ones.

Keywords: Korovkin theorem, relative uniform convergence, bivariate Kantorovich operator

Full Text: PDF