On Iλ-Statistical Convergence in Locally Solid Riesz Spaces

Das P., Savas E.

Mathematica Slovaca, vol.65, no.6, pp.1491-1504, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 65 Issue: 6
  • Publication Date: 2015
  • Doi Number: 10.1515/ms-2015-0101
  • Journal Name: Mathematica Slovaca
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1491-1504
  • Keywords: filter, I-statistical-τ-convergence, ideal, Iλ-statistical-τ-boundedness, Iλ-statistical-τ-Cauchy condition, Iλ-statistical-τ-continuity, Iλ-statistical-τ-convergence
  • Uşak University Affiliated: No

Abstract

In this paper, we extend some results concerning statistical convergence in locally solid Riesz spaces by introducing a more general idea of convergence, namely Iλ-statistical convergence. We investigate the ideas of Iλ-statistical-τ-convergence, Iλ-statistical-τ-boundedness and Iλ-statistical-τ-Cauchy condition of sequences in a locally solid Riesz space endowed with a topology τ and investigate some of their consequences.