A New Class of Sequences Related to the Spaces Defined by Sequences of Orlicz Functions

Naiml Braha

doi:10.1155/2011/539745

Abstract

We introduce new sequence space defined by combining an Orlicz function, seminorms, and -sequences. We study its different properties and obtain some inclusion relation involving the space Inclusion relation between statistical convergent sequence spaces and Cesaro statistical convergent sequence spaces is also given.

Highlights

By w, we denote the space of all real or complex valued sequences
And in the sequel, we will use the convention that any term with a negative subscript is equal to naught, for example, λ−1 0 and x−1 0
Sargent 2 studied some of its properties and obtained its relationship with the space lp

Summary

Introduction

We denote the space of all real or complex valued sequences. We will write l∞, c, and c0 for the sequence spaces of all bounded, convergent, and null sequences, respectively. By lp 1 ≤ p < ∞ , we denote the sequence space of all p-absolutely convergent series, that is, lp {x xk ∈ w :. And lp X denote, respectively, the spaces of all, bounded, and p-absolutely summable sequences with the elements in X, where X, q is a seminormed space. And in the sequel, we will use the convention that any term with a negative subscript is equal to naught, for example, λ−1 0 and x−1 0 It is well known 1 that if limnxn a in the ordinary sense of convergence, lim n. We deduce that the ordinary convergence implies the λ-convergence to the same limit

Definitions and Background

Results

Statistical Convergence

Cesaro Convergence