Some Generalized Difference Sequence Spaces Defined by Ideal Convergence and Musielak-Orlicz Function

Awad A Bakery,Elsayed Abdelbayen Elnour Mohamed,Mohamed Alamin Ahmed

doi:10.1155/2013/972363

Abstract

In the present paper we introduced the ideal convergence of generalized difference sequence spaces combining de La Vallée-Poussin mean and Musielak-Orlicz function overn-normed spaces. We also study some topological properties and inclusion relation between these spaces.

Highlights

Throughout the paper ω, l∞, c, c0, and lp denote the classes of all, bounded, convergent, null, and p-absolutely summable sequences of complex numbers
We find out some relations related to these sequence spaces
Let I be an admissible ideal of N, M = (Mj) be a Musielak-Orlicz function, and (X, ‖⋅, . . . , ⋅‖) an n-normed space

Summary

Introduction

Throughout the paper ω, l∞, c, c0, and lp denote the classes of all, bounded, convergent, null, and p-absolutely summable sequences of complex numbers. Kızmaz [17] defined the difference sequence spaces l∞(Δ), c(Δ), and c0(Δ) as follows: Z(Δ) = {x = (xk) : (Δxk) ∈ Z}, for Z = l∞, c, and c0, where Introduced the following new type of difference sequence spaces. S be nonnegative integers, for Z a given sequence space we have

Objectives

Results

Conclusion