2021/05/31 by Enes Yavuz · 8 citations
Mathematics · #Approximation Theory and Sequence Spaces #Combinatorics #Compact convergence #Computer science #Convergence (economics) #Convergence tests #Discrete mathematics #Fixed Point Theorems Analysis #Fuzzy Systems and Optimization #Geometric mean #Geometry #Mathematical analysis #Mathematics #Modes of convergence (annotated index) #Multiplicative function #Normal convergence #Rate of convergence #Sequence (biology) #Topological space #Topological vector space #math.GM
paper · pdf · doi:10.1080/16583655.2022.2071046
published in Journal of Taibah University for Science 16(1), 442-450 (Elsevier BV) · publication information is added, final version
openalex publication_date 2022/05/09 · openalex created_date 2022/05/11 · arxiv created 2022/05/19 · arxiv updated 2022/05/20 · openalex updated_date 2026/05/22
We define weighted geometric mean method of convergence for sequences in [Formula: see text] by using multiplicative calculus and obtain necessary and sufficient conditions under which convergence of sequences in [Formula: see text] 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: see text]convergence, [Formula: see text]convergence, [Formula: see text]convergence, [Formula: see text]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.