Statistical order convergence in Riesz spaces

ŞENÇİMEN C., PEHLİVAN S.

MATHEMATICA SLOVACA, vol.62, no.2, pp.257-270, 2012 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.2478/s12175-012-0007-z
  • Journal Name: MATHEMATICA SLOVACA
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.257-270
  • Keywords: Riesz space, statistical monotone convergence, statistical order convergence, statistical convergence in norm, statistical order boundedness

Abstract

In this paper, we introduce the concepts of statistical monotone convergence and statistical order convergence in a Riesz space, and establish some basic facts. We show that the statistical order convergence and the statistical convergence in norm need not be equivalent in a normed Riesz space. Finally, we introduce the statistical order boundedness of a sequence in a Riesz space.