ON LACUNARY I –INVARIANT CONVERGENCE OF SEQUENCES IN QUATERNION–VALUED GENERALIZED METRIC SPACES
Journal of Classical Analysis, cilt.24, sa.2, ss.111-132, 2024 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 24 Sayı: 2
- Basım Tarihi: 2024
- Doi Numarası: 10.7153/jca-2024-24-06
- Dergi Adı: Journal of Classical Analysis
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.111-132
- Anahtar Kelimeler: ideal convergence, invariant, lacunary sequence, Quaternion-valued g-metric space, statistical convergence
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
In this study, we explore the concept of lacunary Iσ-convergence of sequences and analyze the relationships between this new convergence concept and the notions of lacunary invariant summability, lacunary strongly s-invariant summability, and lacunary σ-statistical convergence, all of which are defined within quaternion-valued generalized metric spaces. Additionally, our paper aims to introduce the concepts of lacunary Iσ∗-convergence in quaternion-valued generalized metric spaces. We then establish the equivalence between lacunary Iσ-convergence and lacunary Iσ∗-convergence by providing the definition of property (AP). Furthermore,we introduce lacunary Iσ-Cauchy and lacunary Iσ∗-Cauchy sequences, adapting classical theorems to quaternion-valued generalized metric spaces.