On generalized difference lacunary statistical convergence in a paranormed space

Selma Altundağ

doi:10.1186/1029-242x-2013-256

Abstract

In this article, we introduce the concept of Δ m -lacunary statistical convergence and Δ m -lacunary strong convergence in a paranormed space. Also, we establish some connections between these concepts.

Highlights

In order to extend convergence of sequences, the notion of statistical convergence was introduced by Fast [ ] and Steinhaus [ ] and several generalizations and applications of this concept have been investigated by various authors [, ]
We study the concept of statistical convergence from difference sequence spaces which are defined over paranormed space
The notion of difference sequence spaces was further generalized by Et and Çolak [ ] as follows: X m = x = ∈ w : mxk ∈ X

Summary

Introduction

In order to extend convergence of sequences, the notion of statistical convergence was introduced by Fast [ ] and Steinhaus [ ] and several generalizations and applications of this concept have been investigated by various authors [ , ]. We study the concept of statistical convergence from difference sequence spaces which are defined over paranormed space. The notion of difference sequence spaces was further generalized by Et and Çolak [ ] as follows: X m = x = (xk) ∈ w : mxk ∈ X

Results

Conclusion