A New Class of Korovkin-Type Theorems on Double Sequences

In this work, we introduce the concept of statistical deferred weighted convergence for double real sequences and use it to establish a Korovkin-type approximation theorem on double sequences of positive linear operators. These operators act on the space of \(2\pi\)-periodic, continuous real-valued functions in two dimensions. We also demonstrate that our results are more robust than those obtained from their single-sequence statistical and classical counterparts. Furthermore, we examine the rates of statistical deferred weighted convergence with the same set of \(2\pi\)-periodic functions. Finally, we provide several examples to validate our theoretical findings and present suitable graphs via MATLAB software to demonstrate the convergence behaviour of the results under our proposed methods.