Statistical order convergence in Riesz spaces

ŞENÇİMEN C., PEHLİVAN S.

MATHEMATICA SLOVACA, vol.62, no.2, pp.257-270, 2012 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.2478/s12175-012-0007-z
  • Title of Journal : MATHEMATICA SLOVACA
  • Page Numbers: pp.257-270

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.