Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2022, Cilt: 14 Sayı: 2, 331 - 339, 30.12.2022

Jeta Alo

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

Öz

Kaynakça

  • 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

Yıl 2022, Cilt: 14 Sayı: 2, 331 - 339, 30.12.2022

Jeta Alo

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • 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.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Jeta Alo 0000-0002-9149-7811

Erken Görünüm Tarihi 23 Aralık 2022
Yayımlanma Tarihi 30 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 14 Sayı: 2

Kaynak Göster

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. Aralık 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, sy. 2 (Aralık 2022): 331-39. https://doi.org/10.47000/tjmcs.1097599.
EndNote Alo J (01 Aralık 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, c. 14, sy. 2, ss. 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 (Aralık 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, c. 14, sy. 2, 2022, ss. 331-9, doi:10.47000/tjmcs.1097599.
Vancouver Alo J. On Third Order Bronze Fibonacci Quaternions. TJMCS. 2022;14(2):331-9.