Abstract

In this paper we consider the notion of $A^\Cal {I}_2$-statistical convergence for real double sequences which is an extension of the notion of $A^\Cal {I}$-statistical convergence for real single sequences introduced by Savas, Das and Dutta. We primarily apply this new notion to prove a Korovkin type approximation theorem. In the last section, we study the rate of $A^\Cal {I}_2$-statistical convergence.

Keywords: Ideal; $A^\Cal {I}_2$-statistical convergence; positive linear operator; Korovkin type approximation theorem; rate of convergence.

MSC: 40A35, 47B38, 41A25, 41A36

Pages:  288$-$300     

Volume  67 ,  Issue  4 ,  2015