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 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:
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