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

Abstract

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