Recently, Kórus  studied the Λ 2-strong convergence of numerical sequences. By using the idea of this paper, we introduce [ Λ 2, F, u, p] -strongly convergent sequence spaces defined by a sequence of modulus functions. We also make an effort to study some inclusion relations, topological and geometric properties of these spaces. Some characterizations for strong convergent sequences are given. Finally, we study statistical convergence over these spaces and problems related to Fourier series. © 2016, Akadémiai Kiadó, Budapest, Hungary.