Korovkin Type Approximation Theorem for Functions of Two Variables Through αβ−Statistical Convergence

Abstract

In this paper, we introduce the concepts of αβ−statistical convergence and strong αβ− summability of double sequences and investigate the relation between these two new concepts. Moreover, statistical convergence and αβ− statistical convergence of double sequences are compared under some certain assumptions. Finally, as an application, we prove Korovkin type approximation theorem for a function of two variables by using the notion of αβ−statistical convergence.

Keywords

• αβ-statistical convergence
• double sequences
• korovkin type theorem
• lacunary statistical convergence
• λ-statistical convergence
• statistical convergence