Some Seminormed Difference Sequence Spaces over n-Normed Spaces Defined by a Musielak-Orlicz Function of Order (α,β)

Dina A Abuzaid,Sunil K Sharma,S A Mohiuddine

doi:10.1155/2018/4312817

Dina A Abuzaid, Sunil K Sharma + Show 1 more

Open Access

https://doi.org/10.1155/2018/4312817

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Abstract

We first define the notion of lacunary statistical convergence of order (α,β), and taking this notion into consideration, we introduce some seminormed difference sequence spaces over n-normed spaces with the help of Musielak-Orlicz function M=(Mk) of order (α,β). We also examine some topological properties and prove inclusion relations between the resulting sequence spaces.

Highlights

Introduction and PreliminariesGahler [1] extended the usual notion of normed spaces into 2-normed spaces, while the notion was again extended to nnormed spaces by Misiak [2]
We first define the notion of lacunary statistical convergence of order (α, β), and taking this notion into consideration, we introduce some seminormed difference sequence spaces over n-normed spaces with the help of Musielak-Orlicz function M = (Mk) of order (α, β)
We examine some topological properties and prove inclusion relations between the resulting sequence spaces

Summary

Introduction

Introduction and PreliminariesGahler [1] extended the usual notion of normed spaces into 2-normed spaces, while the notion was again extended to nnormed spaces by Misiak [2]. We first define the notion of lacunary statistical convergence of order (α, β), and taking this notion into consideration, we introduce some seminormed difference sequence spaces over n-normed spaces with the help of Musielak-Orlicz function M = (Mk) of order (α, β). > 0} , which is called Orlicz sequence space and showed that lM is a Banach space with the following norm:

Results

Conclusion