Statistical e-Convergence of Double Sequences and its Application to Korovkin-Type Approximation Theorem for Functions of Two Variables

Abstract

In this paper, we have introduced the concept of statistical e-convergence and proved some fundamental properties of statistical e-convergence. In addition, we have introduced strongly \(e\texttt {-}|C_{10}|\)-summability and examined the relationship between statistical e-convergence and strongly \(e\texttt {-}|C_{10}|\)-summability of double sequences. Finally, we investigate a Korovkin-type approximation theorem for double sequences of positive linear operators on the space of all continuous real-valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version.