Statistically Bornological Convergence
Open Journal of Mathematical Sciences, vol.10, pp.274-282, 2026 (Scopus)
- Publication Type: Article / Article
- Volume: 10
- Publication Date: 2026
- Doi Number: 10.30538/oms2026.0285
- Journal Name: Open Journal of Mathematical Sciences
- Journal Indexes: Scopus
- Page Numbers: pp.274-282
- Keywords: bornological convergence, statistical convergence, statistically bornological convergence, wijsman convergence
- Open Archive Collection: AVESIS Open Access Collection
- İstanbul Ticaret University Affiliated: Yes
Abstract
In this paper, we introduce and investigate the concept of statistically bornological convergence for sequences of subsets in metric spaces. This notion combines the localization principle of bornological convergence with the asymptotic flexibility of statistical convergence. A sequence of sets is said to be statistically bornologically convergent if the bornological inclusion conditions hold for a set of indices with natural density one. We provide examples distinguishing this concept from classical bornological and Hausdorff convergence. Under appropriate boundedness assumptions, we establish a functional characterization using excess functionals. We prove stability under bi-Lipschitz embeddings using a direct inclusion-based approach with properly defined pushforward ideals, and establish a subsequence theorem via the diagonal density lemma. The relationship with Wijsman statistical convergence is clarified.