- W T Sulaiman
^{1}Email author

**2011**:365453

https://doi.org/10.1155/2011/365453

© W. T. Sulaiman. 2011

**Received: **5 November 2010

**Accepted: **19 January 2011

**Published: **26 January 2011

## Abstract

## Keywords

## 1. Introduction

Necessary and sufficient conditions for the method to be regular are

(ii)
, where
is a positive constant independent of
*.*

For , summability reduces to summability.

It is quite reasonable to give the following definition.

holds for (see [3]).

Das [1], in 1966, proved the following result.

Theorem 1.1.

Let , . Then if is -summable, it is -summable.

Recently Singh and Sharma [4] proved the following theorem.

Theorem 1.2.

## 2. Lemmas

## 3. Result

## Authors’ Affiliations

## References

- Das G:
**On some methods of summability.***The Quarterly Journal of Mathematics Oxford Series*1966,**17**(2):244–256.MATHView ArticleGoogle Scholar - Sulaiman WT:
**Notes on two summability methods.***Pure and Applied Mathematika Sciences*1990,**31**(1–2):59–69.MATHMathSciNetGoogle Scholar - Sulaiman WT:
**Extension on absolute summability factors of infinite series.***Journal of Mathematical Analysis and Applications*2006,**322**(2):1224–1230. 10.1016/j.jmaa.2005.09.019MATHMathSciNetView ArticleGoogle Scholar - Singh N, Sharma N:
**On****summability factors of infinite series.***Proceedings of Mathematical Sciences*2000,**110**(1):61–68. 10.1007/BF02829481MATHMathSciNetView ArticleGoogle Scholar

## Copyright

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.