Multidimensional matrix characterization of equivalent double sequences

Patterson R., Savaş E.

Studia Scientiarum Mathematicarum Hungarica, cilt.49, sa.2, ss.269-281, 2012 (SCI-Expanded) identifier

  • 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: asymptotical statistically regular, P-convergent, Primary 42B15, Secondary 40C05
  • Uşak Üniversitesi Adresli: Hayır

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.