On I-asymptotically lacunary statistical equivalent sequences

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Savaş E.

Advances in Difference Equations, cilt.2013, 2013 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2013
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1186/1687-1847-2013-111
  • Dergi Adı: Advances in Difference Equations
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: asymptotical equivalent, ideal convergence, lacunary sequence, statistical convergence
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

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.