Multidimensional matrix characterization of equivalent double sequences
Studia Scientiarum Mathematicarum Hungarica, cilt.49, sa.2, ss.269-281, 2012 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 49 Sayı: 2
- Basım Tarihi: 2012
- Doi Numarası: 10.1556/sscmath.49.2012.2.1206
- Dergi Adı: Studia Scientiarum Mathematicarum Hungarica
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.269-281
- Anahtar Kelimeler: P-convergent, asymptotical statistically regular
- İstanbul Ticaret Üniversitesi Adresli: Evet
Özet
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.