$\Lambda^2$-statistical convergence and its application to Korovkin second theorem

Valdete Loku, Naim Latif Braha


In this paper, we use the notion of strong $(N, \lambda^2)-$summability to generalize the concept of statistical convergence. We call this new method a $\lambda^2-$statistical convergence and denote by $S_{\lambda^2}$ the set of sequences which are $\lambda^2-$statistically convergent. We find its relation to statistical convergence and strong $(N, \lambda^2)-$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 $\lambda^2$-statistically summability and the rate of $\lambda^2$-statistically summability of a sequence of positive linear operators defined from $C_{2\pi}(\mathbb{R})$ into $C_{2\pi}(\mathbb{R}).$


$\Lambda^2-$weighted statistical convergence, Korovkin type theorem, Rate of convergence

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DOI: http://dx.doi.org/10.24193/subbmath.2019.4.08


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