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On a new generalization of Fibonacci quaternions

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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