Multidimensional matrix characterization of equivalent double sequences
Studia Scientiarum Mathematicarum Hungarica, vol.49, no.2, pp.269-281, 2012 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 49 Issue: 2
- Publication Date: 2012
- Doi Number: 10.1556/sscmath.49.2012.2.1206
- Journal Name: Studia Scientiarum Mathematicarum Hungarica
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.269-281
- Keywords: P-convergent, asymptotical statistically regular
- İstanbul Ticaret University Affiliated: Yes
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 with [x] P<0, and [y] P< δ for some δ > 0 then μ(Ax)
μ(Ay). In addition other implications and variations shall also be presented.