ℐ-αβ-statistical relative uniform convergence for double sequences and its applications

This article introduces a novel concept of convergence, referred to as & Iscr; {\mathcal{ {\mathcal I} }} - alpha beta \alpha \beta -statistical relative uniform convergence, for double sequences of functions. This notion, which is proposed for the first time in this article, is explored in depth, leading to the establishment of a Korovkin-type approximation theorem within this framework. The illustrative example demonstrates that the proposed convergence is indeed stronger than previously known forms. Additionally, this article investigates the rate of & Iscr; 2 {{\mathcal{ {\mathcal I} }}}_{2} - alpha beta \alpha \beta -statistical relative uniform convergence, providing explicit computations to support the findings. The results contribute to the understanding of ideal statistical convergence and open up new perspectives for approximation theory.