Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, , 670 - 683, 31.08.2022
https://doi.org/10.18185/erzifbed.1132164

Öz

Kaynakça

  • Asci M., Aydinyuz S., (2021) Generalized k-order Fibonacci and Lucas hybrid numbers, Journal of Information and Optimization Sciences, 42(8), 1765-1782.
  • Asci M., Aydinyuz S., (2021) k-order Fibonacci quaternions, Journal of Science and Arts; Targoviste, 21(1), 29-38.
  • Dağdeviren A., Kürüz F., (2020) On the Horadam hybrid quaternions, https://arXiv.2012.08277.
  • Deveci Ö., Shannon A., (2018) The quaternion-Pell sequence, Communications in Algebra, 46(12), 5403-5409.
  • Gül K., (2019) On bi-periodic Jacobsthal and Jacobsthal-Lucas quaternions, Journal of Mathematics Research ,11(2), 44-52.
  • Gül K., (2020) Dual bicomplex Horadam quaternions, Notes on Number Theory and Discrete Mathematics, 26(4), 187–205.
  • Halici S., (2012) On Fibonacci quaternions, Adv. Appl. Clifford Algebras, 22(2), 321-327.
  • Hamilton W. R., (1866) Elements of quaternions. Longmans, Green and Co., London.
  • Horadam A. F., (1963) Complex Fibonacci numbers and Fibonacci quaternions, Math. Mag., 70(3), 289-291.
  • Kızılateş C., (2020) A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos, Solitons & Fractals, 130.
  • Szynal-Liana A., Wloch I. (2019). The Fibonacci hybrid numbers, Utilitas Math., 110, 3–10.
  • Özdemir M., (2018) Introducion to hybrid numbers, Adv. Appl. Clifford Algebra, 28(1), 11-32.
  • Petroudi S. H. J., Pirouz M., . Karaca E and Yılmaz F., (2021) A combined approach to Perrin and Padovan hybrid sequences, Heliyon, 7 (8).
  • Soykan Y., (2019) Simson Identity of Generalized m-step Fibonacci Numbers, Int. J. Adv. Appl. Math. and Mech., 7(2), 45 – 56.
  • Şentürk T. D., Bilgici G., Daşdemir A. and Ünal Z., (2020) A Study on Horadam Hybrid Numbers, Turkish Journal of Mathematics, 44, 1212-1221.
  • Er M.C., (1984) Sums of Fibonacci numbers by matrix methods, Fibonacci Quart, 22(3), 204-207.
  • Uysal M., Özkan E., (2022) Padovan Hybrid Quaternions and some properties, Journal of Science and Arts, 22(1), 121-132.
  • Kilic E., Dursun T., (2006) On the generalized order-k Fibonacci and Lucas numbers, Rocky Mountain J. Math., 36(6), 1915-1926.
  • Lee G.Y., Lee S.G., Kim J.S., Shin H.K., (2001) The Binet Formula and Representations of k-Generalized Fibonacci Numbers, The Fibonacci Quart. 158-164.
  • Lee G.Y., Lee S.G., (1995) A note on generalized Fibonacci numbers, Fibonacci Quart., 33, 273-278.

Generalized k-Order Fibonacci Hybrid Quaternions

Yıl 2022, , 670 - 683, 31.08.2022
https://doi.org/10.18185/erzifbed.1132164

Öz

In this study, generalized k-order Fibonacci hybrid quaternion is defined. We give recurrence relation, generating function, the summation formula and some properties for these quaternions. Furthermore, the matrix representation for generalized k-order Fibonacci hybrid quaternions is determined. The Q_k matrix defined for k-order Fibonacci numbers is given for the generalized k-order Fibonacci hybrid quaternions. By the means of this matrix and another defined matrices, several identities of these quaternions are also obtained.

Kaynakça

  • Asci M., Aydinyuz S., (2021) Generalized k-order Fibonacci and Lucas hybrid numbers, Journal of Information and Optimization Sciences, 42(8), 1765-1782.
  • Asci M., Aydinyuz S., (2021) k-order Fibonacci quaternions, Journal of Science and Arts; Targoviste, 21(1), 29-38.
  • Dağdeviren A., Kürüz F., (2020) On the Horadam hybrid quaternions, https://arXiv.2012.08277.
  • Deveci Ö., Shannon A., (2018) The quaternion-Pell sequence, Communications in Algebra, 46(12), 5403-5409.
  • Gül K., (2019) On bi-periodic Jacobsthal and Jacobsthal-Lucas quaternions, Journal of Mathematics Research ,11(2), 44-52.
  • Gül K., (2020) Dual bicomplex Horadam quaternions, Notes on Number Theory and Discrete Mathematics, 26(4), 187–205.
  • Halici S., (2012) On Fibonacci quaternions, Adv. Appl. Clifford Algebras, 22(2), 321-327.
  • Hamilton W. R., (1866) Elements of quaternions. Longmans, Green and Co., London.
  • Horadam A. F., (1963) Complex Fibonacci numbers and Fibonacci quaternions, Math. Mag., 70(3), 289-291.
  • Kızılateş C., (2020) A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos, Solitons & Fractals, 130.
  • Szynal-Liana A., Wloch I. (2019). The Fibonacci hybrid numbers, Utilitas Math., 110, 3–10.
  • Özdemir M., (2018) Introducion to hybrid numbers, Adv. Appl. Clifford Algebra, 28(1), 11-32.
  • Petroudi S. H. J., Pirouz M., . Karaca E and Yılmaz F., (2021) A combined approach to Perrin and Padovan hybrid sequences, Heliyon, 7 (8).
  • Soykan Y., (2019) Simson Identity of Generalized m-step Fibonacci Numbers, Int. J. Adv. Appl. Math. and Mech., 7(2), 45 – 56.
  • Şentürk T. D., Bilgici G., Daşdemir A. and Ünal Z., (2020) A Study on Horadam Hybrid Numbers, Turkish Journal of Mathematics, 44, 1212-1221.
  • Er M.C., (1984) Sums of Fibonacci numbers by matrix methods, Fibonacci Quart, 22(3), 204-207.
  • Uysal M., Özkan E., (2022) Padovan Hybrid Quaternions and some properties, Journal of Science and Arts, 22(1), 121-132.
  • Kilic E., Dursun T., (2006) On the generalized order-k Fibonacci and Lucas numbers, Rocky Mountain J. Math., 36(6), 1915-1926.
  • Lee G.Y., Lee S.G., Kim J.S., Shin H.K., (2001) The Binet Formula and Representations of k-Generalized Fibonacci Numbers, The Fibonacci Quart. 158-164.
  • Lee G.Y., Lee S.G., (1995) A note on generalized Fibonacci numbers, Fibonacci Quart., 33, 273-278.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Kübra Gül 0000-0002-8732-5718

Yayımlanma Tarihi 31 Ağustos 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Gül, K. (2022). Generalized k-Order Fibonacci Hybrid Quaternions. Erzincan University Journal of Science and Technology, 15(2), 670-683. https://doi.org/10.18185/erzifbed.1132164