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New Properties and Identities for Fibonacci Finite Operator Quaternions

Author

Listed:
  • Nazlıhan Terzioğlu

    (Department of Mathematics, Zonguldak Bülent Ecevit University, 67100 Zonguldak, Turkey)

  • Can Kızılateş

    (Department of Mathematics, Zonguldak Bülent Ecevit University, 67100 Zonguldak, Turkey)

  • Wei-Shih Du

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan)

Abstract

In this paper, with the help of the finite operators and Fibonacci numbers, we define a new family of quaternions whose components are the Fibonacci finite operator numbers. We also provide some properties of these types of quaternions. Moreover, we derive many identities related to Fibonacci finite operator quaternions by using the matrix representations.

Suggested Citation

  • Nazlıhan Terzioğlu & Can Kızılateş & Wei-Shih Du, 2022. "New Properties and Identities for Fibonacci Finite Operator Quaternions," Mathematics, MDPI, vol. 10(10), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1719-:d:817856
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    References listed on IDEAS

    as
    1. Tan, Elif & Leung, Ho-Hon, 2020. "Some results on Horadam quaternions," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Kızılateş, Can & Kone, Tiekoro, 2021. "On higher order Fibonacci hyper complex numbers," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Pavel Trojovský, 2019. "On Terms of Generalized Fibonacci Sequences which are Powers of their Indexes," Mathematics, MDPI, vol. 7(8), pages 1-10, August.
    4. Tan, Elif & Yilmaz, Semih & Sahin, Murat, 2016. "A note on bi-periodic Fibonacci and Lucas quaternions," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 138-142.
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