Regularity characterization of asymptotically probability equivalent sequences

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Patterson R. F., Savaş E.

Applied Mathematics Letters, vol.22, no.10, pp.1491-1495, 2009 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 10
  • Publication Date: 2009
  • Doi Number: 10.1016/j.aml.2009.01.057
  • Journal Name: Applied Mathematics Letters
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1491-1495
  • Keywords: Asymptotically, Equivalent sequences, Regular matrix
  • Open Archive Collection: AVESIS Open Access Collection
  • İstanbul Ticaret University Affiliated: Yes

Abstract

The notion of asymptotically equivalent sequences was presented by Pobyvanets in 1980. Using this definition, he presented Silverman-Toeplitz-type matrix conditions that ensure that a summability matrix preserves asymptotic equivalency. This work begins with an extension of Pobyvanets' definition of convergence in probability. This definition is also used to present Silverman-Toeplitz-type conditions for ensuring that a summability matrix preserves asymptotic probability equivalence. In addition, we shall also present a Marouf-type characterization of such a sequence space. © 2009 Elsevier Ltd. All rights reserved.