In this paper, we investigate the properties of a specialized class of lacunary sequences defined through the Euler transform within the framework of an n-normed space, employing the Musielak–Orlicz function of order \((\alpha , \beta )\) . By constructing these spaces through Euler and matrix transformations of order \((\alpha , \beta )\) , we aim to develop the structural and topological characteristics that govern the behavior of these sequences and analyse some inclusion relations. Our analysis focuses on how such transformations influence convergence behaviors, embedding new perspectives on functional interactions within n-normed spaces. These insights contribute to a deeper understanding of convergence and stability phenomena, broadening the applicability of Musielak–Orlicz function theory in advanced functional analysis and sequence spaces over order \((\alpha , \beta )\) .
