Korovkin type approximation on an infinite interval via generalized matrix summability method using ideal
DOI:
https://doi.org/10.24193/subbmath.2020.2.06Keywords:
Positive linear operator, Korovkin type approximation theorem, ideal, AI -summable, AI-summable.Abstract
Following the notion of AI -summability method for real sequences [24] we establish a Korovkin type approximation theorem for positive linear operators on UC∗[0, ∞), the Banach space of all real valued uniform continuous functions on [0, ∞) with the property that lim f (x) exists finitely for any f ∈ UC∗[0, ∞). In →∞ the last section, we extend the Korovkin type approximation theorem for positive linear operators on UC∗ ([0, ∞) × [0, ∞)). We then construct an example which shows that our new result is stronger than its classical version.
Mathematics Subject Classification (2010): 40A35, 47B38, 41A25, 41A36.
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