Multidimensional matrix characterization of equivalent double sequences
Document Type
Article
Publication Date
6-1-2012
Abstract
In 1936 Hamilton presented a Silverman-Toeplitz type characterization of c″0 (i.e. the space of bounded double Pringsheim null sequences). In this paper we begin with the presentation of a notion of asymptotically statistical regular. Using this definition and the concept of maximum remaining difference for double sequence, we present the following Silverman-Toeplitz type characterization of double statistical rate of convergence: let A be a nonnegative c″0-c″0 summability matrix and let [x] and [y] be member of l″ such that htmlnonpaginated&src=572317679G4412V5-html\MediaObjects/12-2012-1206-Fig1- HTML.gif border=0/> with [x] P 0 then μ(Ax) htmlnonpaginated&src=572317679G4412V5-html\MediaObjects/12-2012-1206-Fig2- HTML.gif border=0/> μ(Ay). In addition other implications and variations shall also be presented.
Publication Title
Studia Scientiarum Mathematicarum Hungarica
Volume
49
Issue
2
First Page
269
Last Page
281
Digital Object Identifier (DOI)
10.1556/SScMath.49.2012.2.1206
ISSN
00816906
E-ISSN
15882896
Citation Information
Patterson, & Savaş, E. (2012). Multidimensional matrix characterization of equivalent double sequences. Studia Scientiarum Mathematicarum Hungarica, 49(2), 269–281. https://doi.org/10.1556/sscmath.49.2012.2.1206