Necessary and Sufficient Conditions for the Equivalence of Statistical, Ideal, and Standard Convergence in G-Metric Spaces
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i1.5608Keywords:
Statistical convergence, ideal convergence, standard convergence, G-metric spaces, necessary and sufficient conditions, equivalence theoremsAbstract
This paper investigates the conditions for equivalence between statistical convergence, ideal convergence, and standard convergence in G-metric spaces. Although the study of statistical and ideal convergence has been extensively developed in various settings, no prior research has explicitly explored the relationship between statistical convergence and standard convergence within G-metric spaces. By addressing this gap, we establish necessary and sufficient conditions for the equivalence of these types of convergence in G-metric spaces. Our results contribute to a deeper understanding of the interplay between these convergence notions and extend the theory of convergence in generalized metric spaces.
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Copyright (c) 2025 Manuharawati Manuharawati, Muhammad Jakfar, Ahmad Taufik Hamzah
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