KOROVKIN TYPE APPROXIMATION THEOREM ON AN INFINITE INTERVAL IN AI-STATISTICAL SENSE.

In this paper, we consider the notion of AI-statistical convergence for real sequences and establish a Korovkin type approximation theorem for positive linear operators on UC*[0;1), the Banach space of all real valued uniform continuous functions on [0;∞) with the property that limx!∞ f(x) exists finitely for any f 2 UC*[0;∞). We then construct an example which shows that our new result is stronger than its classical version. In the section 3, we extend the Korovkin type approximation theorem for positive linear operators on UC*([0;∞) × [0;∞)). [ABSTRACT FROM AUTHOR]