Some Lacunary Sequence Spaces of Invariant Means Defined by Musielak-Orlicz Functions on 2-Norm Space

Mohammad Aiyub

doi:10.4236/am.2014.516248

Abstract

The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.

Highlights

Let ω be the set of all sequences of real numbers ∞, c and c0 be respectively the Banach spaces of bounded, convergent and null sequences x = with ∈ or the usual norm x = supk xk, where k ∈ =1, 2,3, the positive integers.The idea of difference sequence spaces was first introduced by Kizmaz [1] and the concept was generalized by Et and Çolak [2]
Later on Et and Esi [3] extended the difference sequence spaces to the sequence spaces:
Lindenstrauss and Tzafriri [12] used the idea of Orlicz function and defined the sequence space which was called an Orlicz sequence space M such as

Summary

Introduction

Let ω be the set of all sequences of real numbers ∞ , c and c0 be respectively the Banach spaces of bounded, convergent and null sequences x = ( xk ) with ( xk ) ∈ or the usual norm x = supk xk , where k ∈ =1, 2,3, , the positive integers. (2014) Some Lacunary Sequence Spaces of Invariant Means Defined by Musielak-Orlicz Functions on 2-Norm Space. Lindenstrauss and Tzafriri [12] used the idea of Orlicz function and defined the sequence space which was called an Orlicz sequence space M such as

Objectives

Results

Conclusion