ON IDEAL CONVERGENCE OF SEQUENCES IN QUATERNION VALUED GENERALIZED METRIC SPACES
Journal of Mathematical Analysis, vol.15, no.5, pp.19-42, 2024 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 15 Issue: 5
- Publication Date: 2024
- Doi Number: 10.54379/jma-2024-5-2
- Journal Name: Journal of Mathematical Analysis
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.19-42
- Keywords: ideal Cauchy sequence, ideal convergence, Quaternion valued g-metric space
- Süleyman Demirel University Affiliated: Yes
Abstract
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.