Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 2 Sayı: 2, 59 - 64, 28.06.2019
https://doi.org/10.32323/ujma.473514

Öz

Kaynakça

  • [1] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, American Math. Monthly 70(1963), 289-291.
  • [2] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Proc., New York-Toronto, 2001.
  • [3] S. Vajda, Fibonacci and Lucas Numbers the Golden Section, Ellis Horrowood Limited Publ., England, 1989.
  • [4] G. Berzsenyi, Sums of Product of Generalized Fibonacci Numbers, Fibonacci Quart., 13(4), (1975), 343-344.
  • [5] A. F. Horadam, A Generalized Fibonacci sequence, American Math. Monthly, 68, (1961), 455-459.
  • [6] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3(3), (1965), 161-176.
  • [7] M. R. Iyer, Identities involving generalized Fibonacci numbers, Fibonacci Quart., 7(1), (1969), 66-73.
  • [8] J. E. Walton and A. F. Horadam, Some further identities for the generalized Fibonacci sequence, Fibonacci Quart., 12(3), (1974), 272-280.
  • [9] F. Catoni, R. Boccaletti, R. Cannata, V. Catoni, E. Nichelatti and P. Zampatti, The Mathematics of Minkowski Space-Time, Birkhauser, Basel, 2008.
  • [10] H. Gargoubi and S. Kossentini, f-algebra structure on hyperbolic numbers, Adv. Appl. Clifford Algebr., 26(4), (2016), 1211-1233.
  • [11] A. E. Motter and A. F. Rosa, Hyperbolic calculus, Adv. Appl. Clifford Algebr., 8(1), (1998), 109-128.
  • [12] B. Jancewicz, The extended Grassmann algebra of R3, in Clifford (Geometric) Algebras with Applications and Engineering, Birkhauser, Boston, (1996), 389-421.
  • [13] D. Khadjiev and Y. Göksal, Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-Euclidean space, Adv. Appl. Clifford Algebr., 26, (2016), 645-668.
  • [14] A. N. Güncan and Y. Erbil, The q-Fibonacci hyperbolic functions, Appl. Math. Inf. Sci. 8 (1L), (2014), 81-88.
  • [15] L. Barreira, L. H. Popescu and C. Valls, Hyperbolic Sequences of Linear Operators and Evolution Maps, Milan J. Math., 84, (2016), 203-216.
  • [16] J. G. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer-Verlag, 1994.
  • [17] K. Akutagawa and S. Nishikawa, The Gauss Map and Spacelike Surfaces with Prescribed Mean Curvature in Minkowski 3-Space, Th¨oko Math., J., 42, (1990), 67-82.

Hyperbolic Fibonacci Sequence

Yıl 2019, Cilt: 2 Sayı: 2, 59 - 64, 28.06.2019
https://doi.org/10.32323/ujma.473514

Öz

In this paper, we investigate the hyperbolic Fibonacci sequence and the hyperbolic Fibonacci numbers. Furthermore, we give recurrence relations, the golden ratio and Binet's formula for the hyperbolic Fibonacci sequence and Lorentzian inner product, cross product and mixed product for the hyperbolic Fibonacci vectors.

Kaynakça

  • [1] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, American Math. Monthly 70(1963), 289-291.
  • [2] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Proc., New York-Toronto, 2001.
  • [3] S. Vajda, Fibonacci and Lucas Numbers the Golden Section, Ellis Horrowood Limited Publ., England, 1989.
  • [4] G. Berzsenyi, Sums of Product of Generalized Fibonacci Numbers, Fibonacci Quart., 13(4), (1975), 343-344.
  • [5] A. F. Horadam, A Generalized Fibonacci sequence, American Math. Monthly, 68, (1961), 455-459.
  • [6] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3(3), (1965), 161-176.
  • [7] M. R. Iyer, Identities involving generalized Fibonacci numbers, Fibonacci Quart., 7(1), (1969), 66-73.
  • [8] J. E. Walton and A. F. Horadam, Some further identities for the generalized Fibonacci sequence, Fibonacci Quart., 12(3), (1974), 272-280.
  • [9] F. Catoni, R. Boccaletti, R. Cannata, V. Catoni, E. Nichelatti and P. Zampatti, The Mathematics of Minkowski Space-Time, Birkhauser, Basel, 2008.
  • [10] H. Gargoubi and S. Kossentini, f-algebra structure on hyperbolic numbers, Adv. Appl. Clifford Algebr., 26(4), (2016), 1211-1233.
  • [11] A. E. Motter and A. F. Rosa, Hyperbolic calculus, Adv. Appl. Clifford Algebr., 8(1), (1998), 109-128.
  • [12] B. Jancewicz, The extended Grassmann algebra of R3, in Clifford (Geometric) Algebras with Applications and Engineering, Birkhauser, Boston, (1996), 389-421.
  • [13] D. Khadjiev and Y. Göksal, Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-Euclidean space, Adv. Appl. Clifford Algebr., 26, (2016), 645-668.
  • [14] A. N. Güncan and Y. Erbil, The q-Fibonacci hyperbolic functions, Appl. Math. Inf. Sci. 8 (1L), (2014), 81-88.
  • [15] L. Barreira, L. H. Popescu and C. Valls, Hyperbolic Sequences of Linear Operators and Evolution Maps, Milan J. Math., 84, (2016), 203-216.
  • [16] J. G. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer-Verlag, 1994.
  • [17] K. Akutagawa and S. Nishikawa, The Gauss Map and Spacelike Surfaces with Prescribed Mean Curvature in Minkowski 3-Space, Th¨oko Math., J., 42, (1990), 67-82.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Fügen Torunbalcı Aydın 0000-0002-4953-1078

Yayımlanma Tarihi 28 Haziran 2019
Gönderilme Tarihi 22 Ekim 2018
Kabul Tarihi 23 Ocak 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 2

Kaynak Göster

APA Torunbalcı Aydın, F. (2019). Hyperbolic Fibonacci Sequence. Universal Journal of Mathematics and Applications, 2(2), 59-64. https://doi.org/10.32323/ujma.473514
AMA Torunbalcı Aydın F. Hyperbolic Fibonacci Sequence. Univ. J. Math. Appl. Haziran 2019;2(2):59-64. doi:10.32323/ujma.473514
Chicago Torunbalcı Aydın, Fügen. “Hyperbolic Fibonacci Sequence”. Universal Journal of Mathematics and Applications 2, sy. 2 (Haziran 2019): 59-64. https://doi.org/10.32323/ujma.473514.
EndNote Torunbalcı Aydın F (01 Haziran 2019) Hyperbolic Fibonacci Sequence. Universal Journal of Mathematics and Applications 2 2 59–64.
IEEE F. Torunbalcı Aydın, “Hyperbolic Fibonacci Sequence”, Univ. J. Math. Appl., c. 2, sy. 2, ss. 59–64, 2019, doi: 10.32323/ujma.473514.
ISNAD Torunbalcı Aydın, Fügen. “Hyperbolic Fibonacci Sequence”. Universal Journal of Mathematics and Applications 2/2 (Haziran 2019), 59-64. https://doi.org/10.32323/ujma.473514.
JAMA Torunbalcı Aydın F. Hyperbolic Fibonacci Sequence. Univ. J. Math. Appl. 2019;2:59–64.
MLA Torunbalcı Aydın, Fügen. “Hyperbolic Fibonacci Sequence”. Universal Journal of Mathematics and Applications, c. 2, sy. 2, 2019, ss. 59-64, doi:10.32323/ujma.473514.
Vancouver Torunbalcı Aydın F. Hyperbolic Fibonacci Sequence. Univ. J. Math. Appl. 2019;2(2):59-64.

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