On lacunary double statistical convergence in locally solid Riesz spaces

Savas E.

Journal of Inequalities and Applications, vol.2013, 2013 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1186/1029-242x-2013-99
  • Journal Name: Journal of Inequalities and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Double Iθ -statistical-τ-boundedness, Double Iθ -statistical-τ-Cauchy condition, Double Iθ -statistical-τ-convergence, Double I-statistical-τ-convergence, Filter, Ideal
  • Uşak University Affiliated: No

Abstract

The concept of statistical convergence is one of the most active areas of research in the field of summability. Most of the new summability methods have relation with this popular method. In this paper, we introduce the concept of double Iθ -statistical-τ -convergence which is a more general idea of statistical convergence. We also investigate the ideas of double Iθ -statistical-τ -boundedness and double Iθ -statistical-τ -Cauchy condition of sequences in the framework of locally solid Riesz space endowed with a topology τ and investigate some of their consequences. © 2013 Savas; licensee Springer.