Statistical σσ-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 σσ-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 σσ-convergence of a sequence of positive linear operators.