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

Authors : Antonıo BOCCUTO, Kamil DEMİRCİ, Sevda YILDIZ

Pages : 1238-1249

Doi:10.3906/mat-1912-14

View : 11 | Download : 0

Publication Date : 0000-00-00

Article Type : Research Paper

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