Statistical -convergence of positive linear operators

Mursaleen and Edely [M. Mursaleen and O.H.H Edely, On invariant mean and statistical convergence, Appl. Math. Lett. (2009) doi:10.1016/j.aml.2009.06.005] have recently introduced the notion of statistical σ -convergence. In this paper, we study its use in the Korovkin-type approximation theorem. Then, we construct an example such that our new result works but its classical and statistical cases do not work. We also compute the rates of statistical σ -convergence of a sequence of positive linear operators.