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Year 2019, Volume: 2 Issue: 2, 162 - 172, 20.12.2019
https://doi.org/10.33401/fujma.617415

Abstract

References

  • [1] A. Cihan, A. Z. Azak, M. A. G¨ung¨or, M. Tosun, Investigation of Dual-hyperbolic Fibonacci, Dual-hyperbolic Lucas Numbers and their properties. An. Ştiin. Univ. “Ovidius” Constant¸a Ser. Mat., 27(1), 35–48(2019).
  • [2] A. F. Horadam, A generalized Fibonacci sequence, Amer. Math. Monthly, 68 (1961), 455–459.
  • [3] A. L. Iakini, Generalized quaternions of higher order, Fibonacci Quart., 15 (1977), 343–346.
  • [4] S. Y¨uce, F. Aydın Torunbalcı, A new aspect of dual Fibonacci quaternions, Adv. Appl. Clifford Algebr., 26 (2015), 873–884.
  • [5] F. Torunbalcı Aydın, Hyperbolic Fibonacci sequence, Univers. J. Math. Appl., 2(2) (2019), 59-64.
  • [6] F. Messelmi, Dual-complex numbers and their Holomorphic functions, https://hal.archives-ouvertes.fr/hal-01114178, (2015).
  • [7] T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley and Sons Publication, New York, 2001.

On Dual-Hyperbolic Numbers with Generalized Fibonacci and Lucas Numbers Components

Year 2019, Volume: 2 Issue: 2, 162 - 172, 20.12.2019
https://doi.org/10.33401/fujma.617415

Abstract

Dual-hyperbolic Fibonacci and Lucas numbers with Fibonacci and Lucas coefficients are introduced by Cihan et al. and some identities and theorems are given regarding modules and conjugates of these numbers. Later, generating function and Binet's formula with the help of this generating function have been derived. Also, Binet formula, Cassini's, Catalan's, d'Ocagne's, Honsberger and Tagiuri identities are found for dual-hyperbolic numbers with generalized Fibonacci and Lucas coefficients. While these operations are being done, we will benefit from the well-known Fibonacci and Lucas identities. Moreover, it is seen that the results which are obtained for the values $p = 1$ and $q = 0$ corresponds to the theorems in the article by Cihan et al.  [1].

References

  • [1] A. Cihan, A. Z. Azak, M. A. G¨ung¨or, M. Tosun, Investigation of Dual-hyperbolic Fibonacci, Dual-hyperbolic Lucas Numbers and their properties. An. Ştiin. Univ. “Ovidius” Constant¸a Ser. Mat., 27(1), 35–48(2019).
  • [2] A. F. Horadam, A generalized Fibonacci sequence, Amer. Math. Monthly, 68 (1961), 455–459.
  • [3] A. L. Iakini, Generalized quaternions of higher order, Fibonacci Quart., 15 (1977), 343–346.
  • [4] S. Y¨uce, F. Aydın Torunbalcı, A new aspect of dual Fibonacci quaternions, Adv. Appl. Clifford Algebr., 26 (2015), 873–884.
  • [5] F. Torunbalcı Aydın, Hyperbolic Fibonacci sequence, Univers. J. Math. Appl., 2(2) (2019), 59-64.
  • [6] F. Messelmi, Dual-complex numbers and their Holomorphic functions, https://hal.archives-ouvertes.fr/hal-01114178, (2015).
  • [7] T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley and Sons Publication, New York, 2001.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mehmet Ali Güngör 0000-0003-1863-3183

Arzu Cihan This is me

Publication Date December 20, 2019
Submission Date September 9, 2019
Acceptance Date October 24, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Güngör, M. A., & Cihan, A. (2019). On Dual-Hyperbolic Numbers with Generalized Fibonacci and Lucas Numbers Components. Fundamental Journal of Mathematics and Applications, 2(2), 162-172. https://doi.org/10.33401/fujma.617415
AMA Güngör MA, Cihan A. On Dual-Hyperbolic Numbers with Generalized Fibonacci and Lucas Numbers Components. Fundam. J. Math. Appl. December 2019;2(2):162-172. doi:10.33401/fujma.617415
Chicago Güngör, Mehmet Ali, and Arzu Cihan. “On Dual-Hyperbolic Numbers With Generalized Fibonacci and Lucas Numbers Components”. Fundamental Journal of Mathematics and Applications 2, no. 2 (December 2019): 162-72. https://doi.org/10.33401/fujma.617415.
EndNote Güngör MA, Cihan A (December 1, 2019) On Dual-Hyperbolic Numbers with Generalized Fibonacci and Lucas Numbers Components. Fundamental Journal of Mathematics and Applications 2 2 162–172.
IEEE M. A. Güngör and A. Cihan, “On Dual-Hyperbolic Numbers with Generalized Fibonacci and Lucas Numbers Components”, Fundam. J. Math. Appl., vol. 2, no. 2, pp. 162–172, 2019, doi: 10.33401/fujma.617415.
ISNAD Güngör, Mehmet Ali - Cihan, Arzu. “On Dual-Hyperbolic Numbers With Generalized Fibonacci and Lucas Numbers Components”. Fundamental Journal of Mathematics and Applications 2/2 (December 2019), 162-172. https://doi.org/10.33401/fujma.617415.
JAMA Güngör MA, Cihan A. On Dual-Hyperbolic Numbers with Generalized Fibonacci and Lucas Numbers Components. Fundam. J. Math. Appl. 2019;2:162–172.
MLA Güngör, Mehmet Ali and Arzu Cihan. “On Dual-Hyperbolic Numbers With Generalized Fibonacci and Lucas Numbers Components”. Fundamental Journal of Mathematics and Applications, vol. 2, no. 2, 2019, pp. 162-7, doi:10.33401/fujma.617415.
Vancouver Güngör MA, Cihan A. On Dual-Hyperbolic Numbers with Generalized Fibonacci and Lucas Numbers Components. Fundam. J. Math. Appl. 2019;2(2):162-7.

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