On the convergence of sequences in ℝ+ through weighted geometric means via multiplicative calculus and application to intuitionistic fuzzy numbers

YAVUZ E.

Journal of Taibah University for Science, cilt.16, sa.1, ss.442-450, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/16583655.2022.2071046
  • Dergi Adı: Journal of Taibah University for Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.442-450
  • Anahtar Kelimeler: Convergence of sequences, multiplicative calculus, weighted geometric means, intuitionistic fuzzy numbers
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

We define weighted geometric mean method of convergence for sequences in (Formula presented.) by using multiplicative calculus and obtain necessary and sufficient conditions under which convergence of sequences in (Formula presented.) follows from convergence of their weighted geometric means. We also obtain multiplicative analogues of Schmidt type slow oscillation condition and Landau type two-sided condition for the convergence in particular. Besides, we introduce the concepts of (Formula presented.) convergence, (Formula presented.) convergence, (Formula presented.) convergence, (Formula presented.) convergence for sequences of intuitionistic fuzzy numbers (IFNs) and apply the aforementioned conditions to achieve convergence in intuitionistic fuzzy number space. Examples of sequences are also given to illustrate the proposed methods of convergence.