On I-asymptotically lacunary statistical equivalent sequences

Savaş E.

Advances in Difference Equations, vol.2013, 2013 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-1847-2013-111
  • Journal Name: Advances in Difference Equations
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Asymptotical equivalent, Ideal convergence, Lacunary sequence, Statistical convergence
  • Uşak University Affiliated: No

Abstract

This paper presents the following definition, which is a natural combination of the definitions for asymptotically equivalent, I-statistically limit and I-lacunary statistical convergence. Let θ be a lacunary sequence; the two nonnegative sequences x = (xκ) and y = (yκ) are said to be I-asymptotically lacunary statistical equivalent of multiple L provided that for every ε > 0, and δ > 0, {r ε ℕ : 1/hr|{k ε Ir :|xk/yk - L|≥ ε}| ≥ δ}εI (denoted by x SLθ(I)~ y) and simply I-asymptotically lacunary statistical equivalent if L = 1. © 2013 Savaş licensee Springer.