Strong Ideal convergence in topological spaces

We define two convergence techniques in this study: statistical $A_{\mathcal{T}} $-strong convergence and $ A^{\mathcal{I}}_{\mathcal{T}} $-strong convergence, both of which are generalizations of $A_{\mathcal{T}} $-strong convergence in Hausdorff topological spaces via a certain class of special functions. Similar to the classic scenario, we find some correlations between $ A^{\mathcal{I}} $-statistical convergence and $ A^{\mathcal{I}}_{\mathcal{T}} $-strong convergence. Additionally, we obtain a characterization of $ A^{\mathcal{I}} $-statistical convergence.