Ideal $e\mbox{-}$Convergence of Double Sequences and A Korovkin-type Approximation Theorem

Abstract

In the present paper, we introduce the concept of ideal $e$-convergence of double sequences and prove some fundamental properties. Next, we define the concepts of ideal $e$-limit superior and inferior for double sequences. After that, some properties of this type of convergence are examined. Finally, we give 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 via ideal $e$-convergence.