Multidimensional matrix characterization of equivalent double sequences

Patterson R., Savaş E.

Studia Scientiarum Mathematicarum Hungarica, vol.49, no.2, pp.269-281, 2012 (SCI-Expanded, Scopus) identifier

  • 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: asymptotical statistically regular, P-convergent, Primary 42B15, Secondary 40C05
  • Uşak University Affiliated: No

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.