Split complex bi-periodic Fibonacci and Lucas numbers

Year 2022, Volume: 71 Issue: 1, 153 - 164, 30.03.2022

Nazmiye Yılmaz

https://doi.org/10.31801/cfsuasmas.704435

Abstract

The initial idea of this paper is to investigate the split complex bi-periodic Fibonacci and Lucas numbers by using SCFLN now on. We try to show some properties of SCFLN by taking into account the properties of the split complex numbers. Then, we present interesting relationships between SCFLN.

Keywords

bi-periodic Fibonacci number, bi-periodic Lucas number, generalized Fibonacci number, split complex number

References

• Aydin, F. T., Hyperbolic Fibonacci sequence, Universal Journal of Mathematics and Applications, 2(2) (2019), 59-64. https://doi.org/10.32323/ujma.473514
• Bala, A., Verma, V., Some properties of bi-variate bi-periodic Lucas polynomials, Annals of the Romanian Society for Cell Biology, 25(4) (2021), 8778-8784. https://www.annalsofrscb.ro/index.php/journal/article/view/3598.
• Bilgici, G., Two generalizations of Lucas sequence, Applied Mathematics and Computation, 245 (2014), 526-538. https://doi.org/10.1016/j.amc.2014.07.111.
• Catoni, F., Boccaletti, R., Cannata, R., Catoni, V., Nichelatti, E., Zampatti, P., The Mathematics of Minkowski Space-Time, Birkhauser, Basel, 2008.
• Dikmen, C.M., Hyperbolic Jacobsthal Numbers, Asian Research Journal of Mathematics, (2019) 1-9. https://doi.org/10.9734/arjom/2019/v15i430153
• Edson, M., Yayenie, O., A new generalization of Fibonacci sequences and extended Binet’s formula, Integers, 9(A48) (2009), 639-654. https://doi.org/10.1515/INTEG.2009.051
• Gargoubi, H., Kossentini, S., f-algebra structure on hyperbolic numbers, Adv. Appl. Clifford Algebr., 26(4) (2016), 1211-1233. https://doi.org/10.1007/s00006-016-0644-3
• Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc, NY, 2001.
• Khadjiev, D., Goksal Y., Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-Euclidean space, Adv. Appl. Clifford Algebr., 26 (2016), 645-668. https://doi.org/10.1007/s00006-015-0627-9
• Khrennikov, A., Segre, G., An Introduction to Hyperbolic Analysis, arxiv, 2005. http://arxiv.org/abs/math-ph/0507053v2.
• Motter, A. E, Rosa, A. F., Hyperbolic calculus, Adv. Appl. Clifford Algebr., 8(1) (1998), 109-128.
• Sobczyk, G., The hyperbolic number plane, The College Mathematics Journal, 26(4) (1995), 268-280.
• Soykan, Y., On hyperbolic numbers with generalized Fibonacci numbers components, preprint, (2019).
• Soykan, Y., Gocen, M., Properties of hyperbolic generalized Pell numbers, Notes on Number Theory and Discrete Mathematics, 26(4) (2020), 136-153. https://doi.org/10.7546/nntdm.2020.26.4.136-153
• Tan, E., Leung, H.H., Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences, Advances in Difference Equations, 2020.1 (2020), 1-11. https://doi.org/10.1186/s13662-020-2507-4
• Tasyurdu, Y., Hyperbolic Tribonacci and Tribonacci-Lucas sequences, International Journal of Mathematical Analysis, 13(12) (2019), 565-572. https://doi.org/10.12988/ijma.2019.91167
• Verma, V., Bala, A., On properties of generalized bi-variate bi-periodic Fibonacci polynomials, International Journal of Advanced Science and Technology, 29(3) (2020), 8065-8072.
• Yayenie, O., A note on generalized Fibonacci sequence, Applied Mathematics and Computation, 217(12) (2011), 5603-5611. https://doi.org/10.1016/j.amc.2010.12.038