Regularity characterization of asymptotically probability equivalent sequences
Applied Mathematics Letters, vol.22, no.10, pp.1491-1495, 2009 (SCI-Expanded, Scopus)
- 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.