A category theorem for double sequences

Patterson R. F., Savas E.

Applied Mathematics Letters, vol.24, no.10, pp.1680-1684, 2011 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 10
  • Publication Date: 2011
  • Doi Number: 10.1016/j.aml.2011.04.017
  • Journal Name: Applied Mathematics Letters
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1680-1684
  • Keywords: Divergent double sequences, P-convergent, P-divergent, Pringsheim limit point, RH-regular, Subsequences of a double sequences
  • Uşak University Affiliated: No

Abstract

The goal of this paper is to present the following multidimensional category theorem for double sequences via four-dimensional matrix transformations. The set of second category double subsequences of the double sequence (sk,l) is summable by a four-dimensional RH-regular matrix A=(am,n,k,l) if and only if (sk,l) is P-convergent. This theorem is established using multidimensional sliding hump constructions for bounded and unbounded doubles sequences. © 2011 Elsevier Ltd. All rights reserved.