Consistent classes of double summability methods
type: Item
instance of: scholarly article
title: Consistent classes of double summability methods
zbMATH Open document ID: 1198.40003
author: Richard F. Patterson
author: Ekrem Savaş
published in: Applied Mathematics Letters
publication date: 2010-06-25T00:00:00Z
review text: The four dimensional matrix \(A\) is said to be RH-regular if it maps every bounded P-convergent sequence into a P-convergent sequence with the same P-limit. The first author [\textit{R F. Patterson}, Int. J. Math. Math. Sci. 23, No.~1, 1--9 (2000; Zbl 0954.40005)] proved that if a bounded double sequence is divergent then there are RH-regular matrix methods that sum it to various values. The authors then ask the following question in this paper: Is there a collection \(\gamma\) of RH-regular matrix methods which are consistent and such that every bounded double sequence is summable by at least one method in the collection? They mention how difficult it is to find all such collections. However, they have extended this class to a countable collection of RH-regular matrix methods with bounded norm.
Mathematics Subject Classification ID: 40B05
Mathematics Subject Classification ID: 40C05
zbMATH DE Number: 5726664
zbMATH Keywords: double sequences
zbMATH Keywords: RH-regular
zbMATH Keywords: Pringsheim convergent
zbMATH Keywords: consistent methods
reviewed by: İbrahím Çanak
MaRDI profile type: Publication
full work available at URL: j.aml.2010.01.028
OpenAlex ID: W1998969544
cites work: Consistent Limitation Methods
cites work: Sets of Consistent Summation Methods
cites work: Analogues of some fundamental theorems of summability theory
DOI: 10.1016/J.AML.2010.01.028
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description: scientific article; zbMATH DE number 5726664