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, vol.16, no.1, pp.442-450, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1080/16583655.2022.2071046
  • Journal Name: Journal of Taibah University for Science
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.442-450
  • Keywords: Convergence of sequences, multiplicative calculus, weighted geometric means, intuitionistic fuzzy numbers
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

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.