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On Harmonic Complex Balancing Numbers

Author

Listed:
  • Fatih Yılmaz

    (Department of Mathematics, Haci Bayram Veli University, Ankara 06900, Turkey
    These authors contributed equally to this work.)

  • Aybüke Ertaş

    (Department of Mathematics, Haci Bayram Veli University, Ankara 06900, Turkey
    These authors contributed equally to this work.)

  • Jiteng Jia

    (Department of Mathematics and Statistics, Xidian University, Xi’an 710071, China
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Fatih Yılmaz & Aybüke Ertaş & Jiteng Jia, 2022. "On Harmonic Complex Balancing Numbers," Mathematics, MDPI, vol. 11(1), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:210-:d:1021266
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    References listed on IDEAS

    as
    1. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    2. Seda Yamaç Akbiyik & Mücahit Akbiyik & Fatih Yilmaz, 2021. "One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms," Mathematics, MDPI, vol. 9(5), pages 1-15, March.
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