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

Binod Chandra Tripathy; Hemen Dutta

doi:10.2478/v10309-012-0028-1

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 20 (2012): Issue 1 (May 2012)

By: Binod Chandra Tripathy and Hemen Dutta

Open Access

|May 2013

Abstract

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).

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