Hybrid numbers with the view of multiplicative calculus
KUWAIT JOURNAL OF SCIENCE, sa.53, ss.1-9, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1016/j.kjs.2025.100500
- Dergi Adı: KUWAIT JOURNAL OF SCIENCE
- Derginin Tarandığı İndeksler: Scopus, Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH, Directory of Open Access Journals
- Sayfa Sayıları: ss.1-9
- Ankara Hacı Bayram Veli Üniversitesi Adresli: Evet
Özet
This paper defines a new number system called multiplicative hybrid numbers. A multiplicative hybrid number is one that satisfies the non-commutative multiplication criteria using any combination of multiplicative dual ($\varepsilon_\star ^{2_\star} = 0_\star$), multiplicative complex ($i_\star ^{2_\star} = -_\star 1_\star$), and multiplicative hyperbolic ($h_\star ^{2_\star} = 1_\star$) numbers. Introducing some algebraic properties, the geometry of multiplicative hybrid numbers is then investigated by examining the effects of an involution on multiplicative hybrid numbers. Additionally, the relationships between involutions and anti-involutions of multiplicative hybrid numbers are given in detail. Taking these properties into account, the geometric interpretation is illustrated by several significant figures.