Lambda^2-statistical convergence and its applicationto Korovkin second theorem

Abstract

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 $C_{2\pi}(\mathbb{R}).$