Characterization on some absolute summability factors of infinite series
type: Item
instance of: scholarly article
title: Characterization on some absolute summability factors of infinite series
zbMATH Open document ID: 0949.40014
DOI: 10.1155/S0161171299228177
author: W. T. Sulaiman
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2000-12-03T00:00:00Z
full work available at URL: https://eudml.org/doc/48575
review text: In a previous paper, the author [Proc. Am. Math. Soc. 115, No. 2, 313-317 (1992; Zbl 0756.40006)] defined a series \(\Sigma a_n\) to be summable \(|N,p_n, \varphi_n|_k\), \(k\geq 1\), if \(\sum^\infty_{n=1} \varphi_n^{k-1} |T_n-T_{n-1} |^k <\infty\), where \(T_n=P_n^{-1} \sum^n_{i=0} p_is_i\). By placing certain restrictions on the sequences \(\{p_n\}\), \(\{q_n\}\), \(\{\alpha_n\}\), and \(\{\beta_n\}\), the author, in this paper, obtains necessary and sufficient conditions for the \(|N,q_n, \beta_n |_k\)-summability of \(\Sigma a_n\) to imply the \(|N,p_n, \alpha_n |_k\)-summability of \(\Sigma a_n\varepsilon_n\). Editorial comment: Apart from a few lines added at the end, the paper is identical to the author's paper [Ganita Sandesh 11, No. 1, 1--6 (1997; Zbl 1186.40010)] which is not mentioned here.
Mathematics Subject Classification ID: 40F05
Mathematics Subject Classification ID: 40D15
zbMATH DE Number: 1417980
zbMATH Keywords: absolute summability factors
zbMATH Keywords: series
reviewed by: Billy E. Rhoades
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1417980