Multidimensional characterization of asymptotically Is₂-equivalent sequences

In 1951 Fast [12] introduced the concept statistical convergence of sequences which is a generalization of convergence. Afterward, Kostyrko et al. [14] extended the notion of statistical convergence to ideal convergence and established some basic theorems. Taking inspiration from this new approach, in this paper we introduce the matrix characterization of asymptotically I2-equivalent and asymptotically I2- statistical equivalent double sequences with an up-to-date perspective on multidimensional matrix transformation. Consequently, we will obtain conditions on (am,n,k,l) which assure us that the transformation is asymptotically I2?regular. This will be accomplished through a series of regularity-type theorems.