On the Space of Interval-Valued Riesz Convergent Sequences and Its Applications to Fundamental Properties
Mathematics, vol.14, no.12, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 14 Issue: 12
- Publication Date: 2026
- Doi Number: 10.3390/math14122094
- Journal Name: Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: interval-valued sequences, quasilinear space, Riesz convergent, sequence spaces
- Erciyes University Affiliated: Yes
Abstract
This study aims to define the space of interval-valued Riesz convergent sequences and to provide a detailed analysis of its structural properties. The classical concept of Riesz convergence is generalized to sequences whose terms consist of closed and bounded intervals rather than real numbers. An appropriate metric structure is established on this space, and it is rigorously proven that the space is complete with respect to this metric. Furthermore, the quasilinear structure, certain topological properties, and the inclusion relations of this space with other related spaces are systematically investigated.