On Harmonic Complex Balancing Numbers
Mathematics, vol.11, no.1, 2023 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 11 Issue: 1
- Publication Date: 2023
- Doi Number: 10.3390/math11010210
- Journal Name: Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
- Keywords: balancing number, Binet formula, Cassini identity, complex balancing number, matrix norm
- Open Archive Collection: AVESIS Open Access Collection
- Ankara Haci Bayram Veli University Affiliated: Yes
Abstract
© 2022 by the authors.In the present work, we define harmonic complex balancing numbers by considering well-known balancing numbers and inspiring harmonic numbers. Mainly, we investigate some of their basic characteristic properties such as the Binet formula and Cassini identity, etc. In addition, one type of symmetric matrix family whose entries are harmonic complex balancing numbers is constructed. Additionally, some linear algebraic properties are obtained. Furthermore, some inequalities are stated by exploiting the well-known inequalities between various matrix norms. Finally, we illustrate the results with some numerical examples.