On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary Δnm-statistical convergence

Abstract In this article, we introduce the lacunary difference sequence spaces w 0 (M, θ, Δ n m , p, q), w 1 (M, θ, Δ n m , p, q) and w ∞ (M, θ, Δ n m , p, q) using a sequence M = (Mk) of Orlicz functions and investigate some relevant properties of these spaces. Then, we define and study the notion of q-lacunary Δ n m -statistical convergent sequences. Further, we study the relationship between q-lacunary n m-statistical convergent sequences and Δ n m the spaces w 0 (M, θ, Δ n m , p, q) and w 1 (M, θ, Δ n m , p, q).