Statistical Equi-Equal Convergence Of Double Sequences And Korovkin Type Approximation Theorems

Many researchers have been interested in the concept of statistical convergence. Since statistical convergence is stronger than the classical convergence. Then, F. Móricz has introduced the statistical convergence of double sequences (Arch. Math. 81 no.1, 82-89 (2003)). Korovkin type approximation theorems have been investigated for sequences (or double sequences) of positive linear operators defined on different spaces via several new convergence methods. Also, it is known that, the concepts of statistical equal convergence and equi-statistical convergence are more general than the statistical uniform convergence. In this work a new type of statistical convergence is defined via using the notions of equi-statistical convergence and statistical equal convergence for double sequences to prove a Korovkin type approximation theorems. Show that the theorem is a non-trivial extension of some well-known Korovkin type approximation theorems which were demonstrated by earlier authors. We give an example in support of new definition and result presented in this work. Finally, we calculate the rate of statistical equi-equal convergence of double sequences of positive linear operators.