Λ²-statistical convergence and its application to Korovkin second theorem
DOI:
https://doi.org/10.24193/subbmath.2019.4.08Keywords:
Λ²−weighted statistical convergence, Korovkin type theorem, rate of convergence.Abstract
In this paper, we use the notion of strong (N, λ²)−summability to generalize the concept of statistical convergence. We call this new method a λ²−statistical convergence and denote by S λ₂ the set of sequences which are λ²−statistically convergent. We find its relation to statistical convergence and strong (N, λ²)−summability. We will define a new sequence space and will show that it is Banach space. Also we will prove the second Korovkin type approximation theorem for λ²-statistically summability and the rate of λ²-statistically summability of a sequence of positive linear operators defined from C₂ₙ (R) into C₂ₙ (R).
Mathematics Subject Classification (2010): 40G15, 41A36, 46A45.
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