Necessary and Sufficient Conditions for the Equivalence of Statistical, Ideal, and Standard Convergence in G-Metric Spaces (European Journal of Pure and Applied Mathematics, 2025)
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.
Keywords: Statistical convergence; ideal convergence; standard convergence; G-metric spaces; necessary and sufficient conditions; equivalence theorems