Approximation theorems using the method of $\mathcal{I}_{2}$-statistical convergence

In this study, we utilize the concept of $\mathcal{I}$-statistical convergence for double sequences to establish a general approximation theorem of Korovkin-type for double sequences of positive linear operators $(PLOs)$ mapping from $H_{\omega }\left( X\right) $ to $C_{B}\left( X\right) $ where $% X=\left[ 0,\infty \right) \times \left[ 0,\infty \right) .$ We then present an example that demonstrates the applicability of our new main result in cases where classical and statistical approaches are not sufficient. Furthermore, we compute the convergence rate of these double sequences of positive linear operators by employing the modulus of smoothness.