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

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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… Click to show full 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: convergence; relative uniform; korovkin type; abstract korovkin

Journal Title: Turkish Journal of Mathematics
Year Published: 2020

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