Consistent classes of double summability methods

Patterson R. F., Savaş E.

Applied Mathematics Letters, vol.23, no.8, pp.831-835, 2010 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 8
  • Publication Date: 2010
  • Doi Number: 10.1016/j.aml.2010.01.028
  • Journal Name: Applied Mathematics Letters
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.831-835
  • Keywords: Consistent methods, Double sequences, Pringsheim convergent, RH-regular
  • Uşak University Affiliated: No

Abstract

In 2000 Patterson proved that if a bounded double sequence is divergent then there are RH-regular matrix methods that sum it to various values. It is now natural to ask the following question. Is there a collection γ. 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? Similar to Goffman and Petersen's presentation we will present a class of such a collection. In addition, it is clear from the presentation here that it is extremely difficult to find all such collections. However, we have extended this class to a countable collection of RH-regular matrix methods with bounded norm. © 2010 Published by Elsevier Ltd.