On weighted statistical convergence based on (p,q)-integers and related approximation theorems for functions of two variables

In this work, we first define a difference operator Δp,q[m] of natural order m   with respect to (p,q)(p,q)-integers. We then introduce the concepts of Λp,q[m]-statistical convergence, statistical Λp,q[m]-summability and strong Λp,q[m]-summability of order γ   by the weighted method. Furthermore, based on the definition of statistical Λp,q[m]-summability, we prove a Korovkin type approximation theorem for functions of two variables. By using (p,q)(p,q)-analogue of Bernstein operator of two variables we give an example which shows that proposed method successfully works. Finally, some Voronovskaja type approximation results are obtained.