Unrestricted Gibonacci Hybrid Numbers

Year 2021, Volume: 13 Issue: 1, 51 - 56, 30.06.2021

Göksal Bilgici

Abstract

Gibonacci sequence is a generalization of Fibonacci sequence and hybrid numbers are a mixture of reals, complex, dual and hyperbolic numbers. In this study, we introduce unrestricted Gibonacci hybrid numbers. After giving the definition of unrestricted gibonacci hybrid numbers, we give Binet--like formula for this kind of numbers. We also obtain some identities for unrestricted Gibonacci hybrid numbers.

Keywords

Fibonacci numbers, gibonacci numbers, hybrid numbers

References

• [1] Catarino, P., On k-Pell hybrid numbers, Journal of Discrete Mathematical Sciences and Cryptography, 22(1) (2019), 83–89.
• [2] Kizilates, C., A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos, Solitons and Fractal, 130 (2020), 109449.
• [3] Koshy, T., Fibonacci and Lucas numbers with applications, John Wiley and Sons, New Jersey, 2018.
• [4] Ozdemir, M., Introduction to hybrid numbers, Advances in Applied Cliord Algebras, 28(1) (2018), 11–43.
• [5] Senturk, T. D., Bilgici, G., Dasdemir, A., Unal, Z., A study on Horadam hybrid numbers., Turkish Journal of Mathematics, 44(4) (2020), 1212–1221.
• [6] Szynal–Liana, A., The Horadam hybrid numbers, Discussiones Mathematicae-General Algebra and Applications, 38(1) (2018), 91–98.
• [7] Szynal–Liana, A., Wloch, I., On Pell and Pell-Lucas hybrid numbers, Comment. Math. Prace Mat., 58 (2018), 11-17.
• [8] Szynal–Liana, A., Wloch, I., On Jacobsthal and Jacobsthal-Lucas hybrid numbers, Annales Mathematicae Silesianae, 33(1) (2019), 276-283.
• [9] Tasyurdu, Y., Tribonacci and tribonacci-Lucas hybrid numbers, International Journal of Contemporary Mathematical Sciences, 14(4) (2019), 245-254.
• [10] Tan, E., Ait-Amrane, N.R. On a new generalization of Fibonacci hybrid numbers, arXiv:2006.09727.