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

In this article, we introduce the lacunary difference sequence spaces w₀(M, θ, Δⁿ_m, p, q), w₁(M, θ, Δⁿ_m, p, q) and w_∞(M, θ, Δⁿ_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 Δⁿ_m-statistical convergent sequences. Further, we study the relationship between q-lacunary n m-statistical convergent sequences and Δⁿ_m the spaces w₀(M, θ, Δⁿ_m, p, q) and w₁(M, θ, Δⁿ_m, p, q).