Ideal Convergent Sequence Spaces with Respect to Invariant Mean and a Musielak-Orlicz Function Over n-Normed Spaces

Sunil Sharma

doi:10.28924/2291-8639-16-2018-882

Abstract

In the present paper we defined I-convergent sequence spaces with respect to invariant mean and a Musielak-Orlicz function M = (M_k) over n-normed spaces. We also make an effort to study some topological properties and prove some inclusion relation between these spaces.

Highlights

Introduction and preliminariesLet σ be an injective mapping from the set of the positive integers to itself such that σp(n) = n for all positive integers n and p, where σp(n) = σ(σp−1(n))
In the present paper we defined I-convergent sequence spaces with respect to invariant mean and a Musielak-Orlicz function M = (Mk) over n-normed spaces
An invariant mean or a σ-mean is a continuous linear functional defined on the space ∞ such that for all x = ∈ ∞: (1) If xn ≥ 0 for all n, φ(x) ≥ 0, (2) φ(e) = 1, (3) φ(Sx) = φ(x), where Sx = (xσ(n))

Summary

Introduction

In the present paper we defined I-convergent sequence spaces with respect to invariant mean and a Musielak-Orlicz function M = (Mk) over n-normed spaces. I-convergent, invariant mean, Orlicz function, Musielak-Orlicz function, n-normed space, A- Lindenstrauss and Tzafriri [10] used the idea of Orlicz function to define the following sequence space.

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