IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v82y2016icp1-4.html
   My bibliography  Save this article

On a new generalization of Fibonacci quaternions

Author

Listed:
  • Tan, Elif
  • Yilmaz, Semih
  • Sahin, Murat

Abstract

In this paper, we present a new generalization of the Fibonacci quaternions that are emerged as a generalization of the best known quaternions in the literature, such as classical Fibonacci quaternions, Pell quaternions, k -Fibonacci quaternions. We give the generating function and the Binet formula for these quaternions. By using the Binet formula, we obtain some well-known results. Also, we correct some results in [3] and [4] which have been overlooked that the quaternion multiplication is non commutative.

Suggested Citation

  • Tan, Elif & Yilmaz, Semih & Sahin, Murat, 2016. "On a new generalization of Fibonacci quaternions," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 1-4.
    • Handle: RePEc:eee:chsofr:v:82:y:2016:i:c:p:1-4
    DOI: 10.1016/j.chaos.2015.10.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077915003318
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2015.10.021?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Catarino, Paula, 2015. "A note on h(x) − Fibonacci quaternion polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 1-5.
    2. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tan, Elif & Yilmaz, Semih & Sahin, Murat, 2016. "A note on bi-periodic Fibonacci and Lucas quaternions," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 138-142.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chung-Chuan Chen & Lin-Ling Huang, 2021. "Some New Identities for the Generalized Fibonacci Polynomials by the Q(x) Matrix," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 13(2), pages 1-21, April.
    2. Flaut, Cristina & Savin, Diana, 2019. "Some remarks regarding l-elements defined in algebras obtained by the Cayley–Dickson process," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 112-116.
    3. Natalia Bednarz, 2021. "On ( k , p )-Fibonacci Numbers," Mathematics, MDPI, vol. 9(7), pages 1-13, March.
    4. Yasemin Taşyurdu, 2019. "Generalized (p,q)-Fibonacci-Like Sequences and Their Properties," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(6), pages 1-43, December.
    5. Fatih Yılmaz & Aybüke Ertaş & Jiteng Jia, 2022. "On Harmonic Complex Balancing Numbers," Mathematics, MDPI, vol. 11(1), pages 1-15, December.
    6. Falcón, Sergio & Plaza, Ángel, 2009. "The metallic ratios as limits of complex valued transformations," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 1-13.
    7. Falcon, Sergio, 2016. "The k–Fibonacci difference sequences," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 153-157.
    8. Falcón, Sergio & Plaza, Ángel, 2009. "On k-Fibonacci sequences and polynomials and their derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1005-1019.
    9. E. Gokcen Kocer & Huriye Alsan, 2022. "Generalized Hybrid Fibonacci and Lucas p-numbers," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 948-955, December.
    10. Ye, Xiaoli & Zhang, Zhizheng, 2017. "A common generalization of convolved generalized Fibonacci and Lucas polynomials and its applications," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 31-37.
    11. Halici, Serpil & Karataş, Adnan, 2017. "On a generalization for fibonacci quaternions," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 178-182.
    12. Kocer, E. Gokcen & Tuglu, Naim & Stakhov, Alexey, 2009. "On the m-extension of the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1890-1906.
    13. Fiorenza, Alberto & Vincenzi, Giovanni, 2011. "Limit of ratio of consecutive terms for general order-k linear homogeneous recurrences with constant coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 145-152.
    14. Falcón, Sergio & Plaza, Ángel, 2008. "On the 3-dimensional k-Fibonacci spirals," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 993-1003.
    15. Aydın, Fügen Torunbalcı, 2018. "Dual-complex k-Fibonacci numbers," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 1-6.
    16. Bijendra Singh & Kiran Sisodiya & Farooq Ahmad, 2014. "On the Products of -Fibonacci Numbers and -Lucas Numbers," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-4, June.
    17. Younseok Choo, 2020. "Relations between Generalized Bi-Periodic Fibonacci and Lucas Sequences," Mathematics, MDPI, vol. 8(9), pages 1-10, September.
    18. Pavel Trojovský & Štěpán Hubálovský, 2020. "Some Diophantine Problems Related to k -Fibonacci Numbers," Mathematics, MDPI, vol. 8(7), pages 1-10, June.
    19. Kızılateş, Can, 2020. "A new generalization of Fibonacci hybrid and Lucas hybrid numbers," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    20. Flaut, Cristina & Savin, Diana, 2018. "Some special number sequences obtained from a difference equation of degree three," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 67-71.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:82:y:2016:i:c:p:1-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.