On Third Order Bronze Fibonacci Quaternions

Year 2022, Volume: 14 Issue: 2, 331 - 339, 30.12.2022

Jeta Alo

https://doi.org/10.47000/tjmcs.1097599

Cited By: 1

Abstract

In this study, we define third order bronze Fibonacci quaternions. We obtain the generating functions, the Binet's formula and some properties of these quaternions. We give d'Ocagne's-like and Cassini's-like identity and we use q-determinants for quaternionic matrices to give the Cassini's identity for third order bronze Fibonacci quaternions.

Keywords

Bronze Fibonacci quaternions, generating function, Binet's formula, Cassini's identity

References

• Akbıyık, M, Alo, J., On third order bronze Fibonacci numbers, Mathematics, 9(2021), 2606,.
• Aydın, F.T., Bicomplex Fibonacci quaternions, Chaos, Solitons and Fractals, 106(2018), 147–153.
• Cerda, G., Bicomplex third order Jacobsthal quaternions, arXiv:1809.06979 [math.AC].
• Cerda-Morales, G., Identites for third order Jacobsthal quaternions, Advances in Applied Clifford Algebras, 27(2)(2017), 1043–1053.
• Cerda-Morales, G., Dual third-order Jacobsthal quaternions, Proyecciones Journal of Mathematics, 37(4)(2018), 731–747.
• Cerda-Morales G., Some results on dual third-order Jacobsthal quaternions, Filomat, 33(7)(2019), 1865–1876.
• Gül, K., On the k- Pell quaternions and the k-Pell-Lucas quaternions, Iğdır Üni. Fen Bilimleri Enst. Der. / Iğdır Univ. J. Inst. Sci. & Tech., 8(1)(2018), 23–35.
• Halici, S., On Fibonacci quaternions, Advances in Applied Clifford Algebras, 22(2012), 321–327.
• Halici, S., Karataş, A., On a generalization for Fibonacci quaternions, Chaos, Solitons Fractals, 98(2017), 178–182.
• Halici, S., Cerda-Morales, G., On quaternions-Gaussian Fibonacci numbers and their properties, An. S¸ t. Univ. Ovidius Constanta, 29(1)(2021), 71–82.
• Halici, S., On complex Fibonacci quaternions, Adv. Appl. Clifford Algebras, 23(2013), 105–112.
• Halici, S., On dual Fibonacci quaternions, Selcuk Journal of Applied Mathematics, 15(1)(2013).
• Hamilton, W.R., Elements of Quaternions, London, Logmans, Green&Company, 1866.
• Hoggatt, V.E., Fibonacci and Lucas numbers, Houghton Mifflin Company, 1969.
• Horodam, A.F., Complex Fibonacci numbers and Fibonacci quaternions, Am. Math. Month., 70(3)(1963), 289–291.
• Soykan, Y., On generalized third-order Pell numbers, Asian Journal of Advanced Research and Reports, 6(1)(2019), 1–18.
• Swamy, M.N.S., On generalized Fibonacci quaternions, The Fibonacci Quarterly, 11(5)(1973), 547–550.
• Yüce, S., Aydın, F.T., Generalized dual Fibonacci quaternions, Applied Mathematics E-Notes, 14(2016), 276–289.
• Yamaç Akbıyık, S., Akbıyık, M., Yüce, S. On metallic ratio in Z(p), Mathematical Methods in the Applied Sciences, 42(16)(2019), 5535–5550.
• Zhang, F., Quaternions and matrices of quaternions, Linear Algebra and Its Applications, 251(1997), 21–57.