In this paper we consider the notion of A2 -statistical convergence for real double sequences which is an extension of the notion of AI -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 A2 -statistical convergence.

We define and study λ2-convergence of double sequences of interval numbers defined by Orlicz function and λ2-statistical convergence of double sequences of interval numbers. We also establish some inclusion relations between them.

After F a s t [6] introduced the theory of statistical convergence of a real sequence, it has become popular among mathematicians ([2], [7]–[9], [17]). The ideas of statistical limit superior and limit inferior were first extensively studied by F r i d y and O r h a n [9]. After K o s t y r k o et al. [10] extended the idea of statistical convergence to I-convergence using the concept of an ide...

Abstract – The aim of this paper is to introduce and study a new concept of strong double Δ ) A ( σ convergence sequences with respect to an Orlicz function, and some properties of the resulting sequence spaces were also examined. In addition, we define the Δ ) A ( σ -statistical convergence and establish some connections between the spaces of strong double Δ ) A ( σ -convergence sequences and ...