New Difference Sequence Spaces Defined by Musielak-Orlicz Function

M Mursaleen,A Kılıçman,S A Mohiuddine,Sunil K Sharma

doi:10.1155/2014/691632

Abstract

We introduce new sequence spaces by using Musielak-Orlicz function and a generalizedB∧ μ-difference operator onn-normed space. Some topological properties and inclusion relations are also examined.

Highlights

Introduction and PreliminariesThe notion of the difference sequence space was introduced by Kızmaz [1]
We introduce new sequence spaces by using Musielak-Orlicz function and a generalized B∧μ-difference operator on n-normed space
It was further generalized by Et and Colak [2] as follows: Z(Δμ) = {x = ∈ ω : (Δμxk) ∈ z} for z = l∞, c, and c0, where μ is a nonnegative integer and

Summary

Introduction

Introduction and PreliminariesThe notion of the difference sequence space was introduced by Kızmaz [1]. We introduce new sequence spaces by using Musielak-Orlicz function and a generalized B∧μ-difference operator on n-normed space. Dutta [4] introduced the following difference sequence spaces using a new difference operator: Z (Δ (η)) = {x = (xk) ∈ ω : Δ (η)x ∈ z} for z = l∞, c, c0, (3) The difference sequence spaces have been studied by authors [6,7,8,9,10,11,12,13,14] and references therein.

Results

Conclusion