Description:
The primary objective of this study is to introduce the notion of ideal convergence in quaternion-valued generalized metric spaces. We define I-convergence and I∗-convergence in these spaces and establish their equivalence through the definition of property (AP). Furthermore, we introduce I-Cauchy and I∗-Cauchy sequences, adapting classically theorems to suit quaternion-valued generalized metric spaces. We also present I-statistical convergence, I-lacunary statistical convergence, strong I-Cesàro summability, strong I-lacunary summability, [V, λ](I)-summability, and I-λ-statistically convergen-cein quaternion valued generalized metric spaces, along with their associated properties.