e-core of double sequences

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Sever Y., Talo Ö.

Acta Mathematica Hungarica, vol.144, no.1, pp.236-246, 2014 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 144 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.1007/s10474-014-0447-8
  • Journal Name: Acta Mathematica Hungarica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.236-246
  • Keywords: double sequence space, e-convergence, e-limit superior and inferior, core theorem
  • Open Archive Collection: AVESIS Open Access Collection
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

Boos, Leiger and Zeller [1,2] defined the concept of e-convergence. In this paper we introduce the concepts of e-limit superior and inferior for real double sequences and prove some fundamental properties of e-limit superior and inferior. In addition to these results we define e-core for double sequences. Also, we show that that if A is a nonnegative Ceregular matrix then the e-core of Ax is contained in e-core of x, provided that Ax exists.