Research Article
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Year 2022, Volume: 14 Issue: 2, 331 - 339, 30.12.2022
https://doi.org/10.47000/tjmcs.1097599

Abstract

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.

On Third Order Bronze Fibonacci Quaternions

Year 2022, Volume: 14 Issue: 2, 331 - 339, 30.12.2022
https://doi.org/10.47000/tjmcs.1097599

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.

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.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Jeta Alo 0000-0002-9149-7811

Early Pub Date December 23, 2022
Publication Date December 30, 2022
Published in Issue Year 2022 Volume: 14 Issue: 2

Cite

APA Alo, J. (2022). On Third Order Bronze Fibonacci Quaternions. Turkish Journal of Mathematics and Computer Science, 14(2), 331-339. https://doi.org/10.47000/tjmcs.1097599
AMA Alo J. On Third Order Bronze Fibonacci Quaternions. TJMCS. December 2022;14(2):331-339. doi:10.47000/tjmcs.1097599
Chicago Alo, Jeta. “On Third Order Bronze Fibonacci Quaternions”. Turkish Journal of Mathematics and Computer Science 14, no. 2 (December 2022): 331-39. https://doi.org/10.47000/tjmcs.1097599.
EndNote Alo J (December 1, 2022) On Third Order Bronze Fibonacci Quaternions. Turkish Journal of Mathematics and Computer Science 14 2 331–339.
IEEE J. Alo, “On Third Order Bronze Fibonacci Quaternions”, TJMCS, vol. 14, no. 2, pp. 331–339, 2022, doi: 10.47000/tjmcs.1097599.
ISNAD Alo, Jeta. “On Third Order Bronze Fibonacci Quaternions”. Turkish Journal of Mathematics and Computer Science 14/2 (December 2022), 331-339. https://doi.org/10.47000/tjmcs.1097599.
JAMA Alo J. On Third Order Bronze Fibonacci Quaternions. TJMCS. 2022;14:331–339.
MLA Alo, Jeta. “On Third Order Bronze Fibonacci Quaternions”. Turkish Journal of Mathematics and Computer Science, vol. 14, no. 2, 2022, pp. 331-9, doi:10.47000/tjmcs.1097599.
Vancouver Alo J. On Third Order Bronze Fibonacci Quaternions. TJMCS. 2022;14(2):331-9.