On Ideal Convergence in Generalized Metric Spaces

Abstract

Our main goal in this paper is to introduce the concept of ideal convergence in G-metric spaces. We give definitions of GI-convergence and GI*-convergence in G-metric spaces. We also extend the I-convergence concept's properties to GI-convergence. Then we demonstrate that GI-convergence and GI*-convergence are equivalent by giving the property (AP) definition. Additionally we introduce GI-Cauchy and GI*-Cauchy sequences and adapt the classically stated theorems to G-metric spaces.