<abstract xmlns="http://www.w3.org/1999/xhtml"> 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).</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).

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

Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Paschim Boragaon, Garchuk, Guwahati-781013, Assam, India

Department of Mathematics, Gauhati University Campus, Kokrajhar-783370, Assam, India

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

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 =...

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

Published Online: May 17, 2013

Page range: 417 - 430

DOI: https://doi.org/10.2478/v10309-012-0028-1

Keywords
Orlicz function, lacunary sequence, seminorm, statistical convergence

This content is open access.