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

Authors : Antonıo Boccuto, Kamil Demirci, Sevda Yildiz

Pages : 1238-1249

Doi:10.3906/mat-1912-14

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Publication Date : 9999-12-31

Article Type : Makaleler

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