Banach Contractive Mapping Theorem on Partially Ordered Sets Equipped with Vector Metric
Turkish Journal of Mathematics and Computer Science, vol.17, no.2, pp.586-594, 2025 (Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 17 Issue: 2
- Publication Date: 2025
- Doi Number: 10.47000/tjmcs.1567340
- Journal Name: Turkish Journal of Mathematics and Computer Science
- Journal Indexes: Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.586-594
- Ankara Yıldırım Beyazıt University Affiliated: Yes
Abstract
Abstract. In this paper, left (right) vector metric convergence and left (right) vector metric continuity are defined using the positive and negative parts of a vector-valued metric. These definitions and the obtained new results are applied to the Banach Contractive Mapping Theorem and examined within the framework of order structures, such as partially ordered sets, Archimedean spaces, and Dedekind complete spaces.