ON IDEAL CONVERGENCE OF SEQUENCES IN QUATERNION VALUED GENERALIZED METRIC SPACES
Journal of Mathematical Analysis, cilt.15, sa.5, ss.19-42, 2024 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 15 Sayı: 5
- Basım Tarihi: 2024
- Doi Numarası: 10.54379/jma-2024-5-2
- Dergi Adı: Journal of Mathematical Analysis
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.19-42
- Anahtar Kelimeler: ideal Cauchy sequence, ideal convergence, Quaternion valued g-metric space
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
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.