Bulletin of the
Korean Mathematical Society BKMS

In this paper, we obtain a Korovkin type approximation theorem for double sequences of positive linear operators of two variables from $H_{w}\left( K\right) $ to $C\left( K\right) $ via $A$-statistical convergence. Also, we construct an example such that our new approximation result works but its classical case does not work. Furthermore, we study the rates of $A$ -statistical convergence by means of the modulus of continuity.

Keywords: $A$-statistical convergence for double sequences, positive linear operator, Korovkin type approximation theorem, Meyer-K\{o}nig and Zeller operator, modulus of continuity

MSC numbers: 41A25, 41A36, 47B38