On generalized double statistical convergence in locally solid riesz spaces

Savas E.

Miskolc Mathematical Notes, vol.17, no.1, pp.591-603, 2016 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.18514/mmn.2016.672
  • Journal Name: Miskolc Mathematical Notes
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.591-603
  • Keywords: Double l-statistical -τ-convergence, Double lλ - statistical-τ-continuity, Double lλ-statistical-τ- Cauchy condition, Double lλ-statistical-τ-boundedness, Double lλ-statistical-τ-convergence, Filter, Ideal
  • Uşak University Affiliated: No

Abstract

The concept of statistical convergence is one of the most active area of research in the field of summability. Over the years and under different names statistical convergence has been discussed in the theory of Fourier analysis, ergodic theory and number theory. In this paper, we introduce the idea of double lλ-statistical convergence in a locally solid Riesz space and study some of its properties by using the mathematical tools of the theory of topological vector spaces.