Statistical convergence in a paranormed space

Abdullah Alotaibi,Abdullah M Alroqi

doi:10.1186/1029-242x-2012-39

Abdullah Alotaibi, Abdullah M Alroqi

Open Access

https://doi.org/10.1186/1029-242x-2012-39

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Abstract

In this article, we define the notion of statistical convergence, statistical Cauchy and strongly p-Cesaro summability in a paranormed space. We establish some relations between them. AMS subject classification (2000): 41A10; 41A25; 41A36; 40A05; 40A30.

Highlights

Introduction and preliminariesThe concept of statistical convergence for sequences of real numbers was introduced by Fast [1] and Steinhaus [2] independently in the same year 1951 and since several generalizations and applications of this notion have been investigated by various authors, namely [3,4,5,6,7,8,9,10,11]
This notion was defined in normed spaces by Kolk [12] and in locally convex Hausdorff topological spaces by Maddox [13]
Çakalli [14] extended this notation to topological Hausdorff groups

Summary

Introduction

Introduction and preliminariesThe concept of statistical convergence for sequences of real numbers was introduced by Fast [1] and Steinhaus [2] independently in the same year 1951 and since several generalizations and applications of this notion have been investigated by various authors, namely [3,4,5,6,7,8,9,10,11]. The concept of statistical convergence for sequences of real numbers was introduced by Fast [1] and Steinhaus [2] independently in the same year 1951 and since several generalizations and applications of this notion have been investigated by various authors, namely [3,4,5,6,7,8,9,10,11]. We shall study the concept of statistical convergence, statistical Cauchy, and strongly p-Cesàro summability in a paranormed space.

Results

Conclusion