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Yıl 2021, Cilt: 13 Sayı: 2, 226 - 233, 31.12.2021

Ümit Tokeşer Tuğba Mert Zafer Ünal Göksal Bilgici

https://doi.org/10.47000/tjmcs.780474

Öz

Kaynakça

  • [1] Akkus, I., Kecilioglu, O., Split Fibonacci and Lucas Octonions, Adv. Appl. Clifford Algebras, 25(2015), 517–525.
  • [2] Akyiğit, M., Kösal, H.H., Tosun, M., Fibonacci Generalized Quaternions, Adv. Appl. Clifford Algebras, 24(2014), 631–641.
  • [3] Catarino, P., The Modified Pell and The Modified k-Pell Quaternions and Octonions, Adv. Appl. Clifford Algebras, 26(2)(2016), 577–590.
  • [4] Cimen, C.B., İpek, A., On Pell Quaternions and Pell-Lucas Quaternions, Adv. Appl. Clifford Algebras, 26(2016), 39–51.
  • [5] Flaut, C., Stefanescu, M., Some Equations over Generalized Quaternion and Octonion Division Algebras, Bull. Math. Soc. Sci. Math. Roum., 52(100)(4)(2009), 427–439.
  • [6] Halici, S., On Fibonacci Quaternions, Adv. Appl. Clifford Algebras, 22(2012), 321–327.
  • [7] Horadam, A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, Amer. Math. Monthly, 70(1963), 289–291.
  • [8] Horadam, A.F., Quaternion Recurrence Relations, Ulam Quarterly, 2(1993), 23–33.
  • [9] Iakin, A.L., Generalized Quaternions of Higher Order, Fibonacci Quart, 15(1977), 343–346.
  • [10] Iyer, M.R., A Note on Fibonacci Quaternions, Fibonacci Quart, 3(1969), 225–229.
  • [11] Keçilioğlu, O., Akkus, I., The Fibonacci Octonions, Adv. Appl. Clifford Algebras, 25(2015), 151–158.
  • [12] Koshy, T., Fibonacci and Lucas Numbers with Applications, A Wiley-Interscience Publication, Canada, 2001.
  • [13] Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
  • [14] Ramirez, J.L., Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions, An. St. Univ. Ovidius Constanta, 23(2)(2015), 201–212.
  • [15] Savin, D., Some Properties of Fibonacci numbers, Fibonacci Octonions, and generalized Fibonacci-Lucas Octonions, Adv. Difference Equ., 2015.1(2015), 298.
  • [16] Swamy, M.N.S., On Generalized Fibonacci Quaternions, The Fib. Quarterly, 5(1973), 547–550.
  • [17] Szynal-Liana, A., Wloch, I., The Pell Quaternions and The Pell Octonions, Adv. Appl. Clifford Algebras, 26(2016), 435–440

On Pell and Pell-Lucas Generalized Octonions

Yıl 2021, Cilt: 13 Sayı: 2, 226 - 233, 31.12.2021

Ümit Tokeşer Tuğba Mert Zafer Ünal Göksal Bilgici

https://doi.org/10.47000/tjmcs.780474

Öz

In this study, we gave a generalization on Pell and Pell-Lucas octonions over the algebra $\mathbb{O}(a,b,c)$ where $a,b$ and $c$ are real numbers. For these number sequences, we obtain Binet formulas and gave some well-known identities such as Catalan's identity, Cassini's identity and d'Ocagne's identity.

Anahtar Kelimeler

Generalized octonion Pell octonion Pell-Lucas octonion

Kaynakça

  • [1] Akkus, I., Kecilioglu, O., Split Fibonacci and Lucas Octonions, Adv. Appl. Clifford Algebras, 25(2015), 517–525.
  • [2] Akyiğit, M., Kösal, H.H., Tosun, M., Fibonacci Generalized Quaternions, Adv. Appl. Clifford Algebras, 24(2014), 631–641.
  • [3] Catarino, P., The Modified Pell and The Modified k-Pell Quaternions and Octonions, Adv. Appl. Clifford Algebras, 26(2)(2016), 577–590.
  • [4] Cimen, C.B., İpek, A., On Pell Quaternions and Pell-Lucas Quaternions, Adv. Appl. Clifford Algebras, 26(2016), 39–51.
  • [5] Flaut, C., Stefanescu, M., Some Equations over Generalized Quaternion and Octonion Division Algebras, Bull. Math. Soc. Sci. Math. Roum., 52(100)(4)(2009), 427–439.
  • [6] Halici, S., On Fibonacci Quaternions, Adv. Appl. Clifford Algebras, 22(2012), 321–327.
  • [7] Horadam, A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, Amer. Math. Monthly, 70(1963), 289–291.
  • [8] Horadam, A.F., Quaternion Recurrence Relations, Ulam Quarterly, 2(1993), 23–33.
  • [9] Iakin, A.L., Generalized Quaternions of Higher Order, Fibonacci Quart, 15(1977), 343–346.
  • [10] Iyer, M.R., A Note on Fibonacci Quaternions, Fibonacci Quart, 3(1969), 225–229.
  • [11] Keçilioğlu, O., Akkus, I., The Fibonacci Octonions, Adv. Appl. Clifford Algebras, 25(2015), 151–158.
  • [12] Koshy, T., Fibonacci and Lucas Numbers with Applications, A Wiley-Interscience Publication, Canada, 2001.
  • [13] Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
  • [14] Ramirez, J.L., Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions, An. St. Univ. Ovidius Constanta, 23(2)(2015), 201–212.
  • [15] Savin, D., Some Properties of Fibonacci numbers, Fibonacci Octonions, and generalized Fibonacci-Lucas Octonions, Adv. Difference Equ., 2015.1(2015), 298.
  • [16] Swamy, M.N.S., On Generalized Fibonacci Quaternions, The Fib. Quarterly, 5(1973), 547–550.
  • [17] Szynal-Liana, A., Wloch, I., The Pell Quaternions and The Pell Octonions, Adv. Appl. Clifford Algebras, 26(2016), 435–440
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik, Mühendislik
Bölüm Makaleler
Yazarlar

Ümit Tokeşer 0000-0003-4773-8291

Tuğba Mert 0000-0001-8258-8298

Zafer Ünal 0000-0003-2445-1028

Göksal Bilgici 0000-0001-9964-5578

Yayımlanma Tarihi 31 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 13 Sayı: 2

Kaynak Göster

APA Tokeşer, Ü., Mert, T., Ünal, Z., Bilgici, G. (2021). On Pell and Pell-Lucas Generalized Octonions. Turkish Journal of Mathematics and Computer Science, 13(2), 226-233. https://doi.org/10.47000/tjmcs.780474
AMA Tokeşer Ü, Mert T, Ünal Z, Bilgici G. On Pell and Pell-Lucas Generalized Octonions. TJMCS. Aralık 2021;13(2):226-233. doi:10.47000/tjmcs.780474
Chicago Tokeşer, Ümit, Tuğba Mert, Zafer Ünal, ve Göksal Bilgici. “On Pell and Pell-Lucas Generalized Octonions”. Turkish Journal of Mathematics and Computer Science 13, sy. 2 (Aralık 2021): 226-33. https://doi.org/10.47000/tjmcs.780474.
EndNote Tokeşer Ü, Mert T, Ünal Z, Bilgici G (01 Aralık 2021) On Pell and Pell-Lucas Generalized Octonions. Turkish Journal of Mathematics and Computer Science 13 2 226–233.
IEEE Ü. Tokeşer, T. Mert, Z. Ünal, ve G. Bilgici, “On Pell and Pell-Lucas Generalized Octonions”, TJMCS, c. 13, sy. 2, ss. 226–233, 2021, doi: 10.47000/tjmcs.780474.
ISNAD Tokeşer, Ümit vd. “On Pell and Pell-Lucas Generalized Octonions”. Turkish Journal of Mathematics and Computer Science 13/2 (Aralık 2021), 226-233. https://doi.org/10.47000/tjmcs.780474.
JAMA Tokeşer Ü, Mert T, Ünal Z, Bilgici G. On Pell and Pell-Lucas Generalized Octonions. TJMCS. 2021;13:226–233.
MLA Tokeşer, Ümit vd. “On Pell and Pell-Lucas Generalized Octonions”. Turkish Journal of Mathematics and Computer Science, c. 13, sy. 2, 2021, ss. 226-33, doi:10.47000/tjmcs.780474.
Vancouver Tokeşer Ü, Mert T, Ünal Z, Bilgici G. On Pell and Pell-Lucas Generalized Octonions. TJMCS. 2021;13(2):226-33.