Some summability factor theorems for absolute summability

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 2002Publisher:Walter de Gruyter GmbHJournal:Analysis, volume 22, pages 163-174 (issn: 0174-4747, eissn: 2196-6753,

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Authors: Rhoades, B. E.; Savaş, Ekrem;

doi: 10.1524/anly.2002.22.2.163

Some summability factor theorems for absolute summability

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Abstract

The authors obtain a set of sufficient conditions on methods of summability and on sequences \(\left(e_n\right)\), so that \(\sigma a_n\) summable \(\left|\overline N,p_n\right|_k\) implies \(\sigma a_n e_n\) summable \(\left|T\right|_k\), with \(k\) greater than or equal to 1. As corollaries they obtain the results of \textit{W. T. Sulaiman} [Proc. Am. Math. Soc. 115, 313-317 (1992; Zbl 0756.40006)].

Keywords

Convergence factors and summability factors, Special methods of summability, absolute summability, Absolute and strong summability

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