Abstract
Fibonacci kuaterniyonları ve bu kuaterniyonların genelleştirmeleri hakkında birçok çalışma göze çarpmaktadır. Geçtiğimiz günlerde Şentürk and Ünal (2022), 3-parametreli genellştirilmiş kuaterniyonları tanıtmışlardır. Bu çalışmada genelleştirilmiş 3-parametreli Fibonacci ve Lucas kuaterniyonları tanıtılmış ve özellikleri araştırılmıştır. Bu kuaterniyonlar için Binet formülleri elde edildikten sonra iyi bilinen bazı özdeşliklerin genelleştirmeleri sunulmuştur.
Keywords
Fibonacci kuaterniyonları Lucas kuaterniyonları Genelleştirilmiş 3-parametreli kuaterniyonlar
References
- Akyiğit, M., Kösal, H. H., & Tosun, M. (2013). Split Fibonacci quaternions. Advances in Applied Clifford Algebras, 23(3), 535-545.
- Akyig̃it, M., Kösal, H. H., & Tosun, M. (2014). Fibonacci generalized quaternions. Advances in Applied Clifford Algebras, 24(3), 631-641.
- Aydın, F. T. (2021). Pauli–Fibonacci quaternions. Notes on Number Theory and Discrete Mathematics, 27(3), 184-193.
- Bilgici, G., Tokeşer, Ü. & Ünal, Z. (2017). k-Fibonacci and k-Lucas generalized quaternıons. Konuralp Journal of Mathematics, 5(2), 102-113
- Flaut, C., & Savin, D. (2015). Quaternion algebras and generalized Fibonacci–Lucas quaternions. Advances in Applied Clifford Algebras, 25(4), 853-862.
- Halici, S. (2012). On Fibonacci quaternions. Advances in Applied Clifford Algebras, 22(2), 321-327.
- Halici, S., & Karataş, A. (2017). On a generalization for Fibonacci quaternions. Chaos, Solitons & Fractals, 98, 178-182.
- Horadam, A. F. (1963). Complex Fibonacci numbers and Fibonacci quaternions. The American Mathematical Monthly, 70(3), 289-291.
- Iyer, M. R. (1969). A note on Fibonacci quaternions. Fibonacci Quart, 7(3), 225-229.
- Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Canada.
- Nurkan, S. K., & Güven, İ. A. (2015). Dual Fibonacci quaternions. Advances in Applied Clifford Algebras, 25(2), 403-414.
- Polatlı, E., Kızılates, C., & Kesim, S. (2016). On split k-Fibonacci and k-Lucas quaternions. Advances in Applied Clifford Algebras, 26(1), 353-362.
- Ramírez, J. L. (2015). Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions. Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, 23(2), 201-212.
- Şentürk, T. D., & Ünal, Z. (2022). 3-parameter generalized quaternions. Computational Methods and Function Theory, 1-34.
- Tan, E., Yilmaz, S., & Sahin, M. (2016). On a new generalization of Fibonacci quaternions. Chaos, Solitons & Fractals, 82, 1-4.
- Yüce, S., & Aydın, F. T. (2016). Generalized dual Fibonacci quaternions. Applied Mathematics E-Notes, 16(30), 276-289.
Abstract
There are many studies on Fibonacci quaternions and their generalizations. Recently, Şentürk and Ünal (2022) introduced 3-parameter generalized quaternions. The goal of this study is to introduce Fibonacci and Lucas 3-parameter generalized quaternions and to investigate their properties. After obtaining Binet formulas for these quaternions, generalizations of some well-known identities are presented.
References
- Akyiğit, M., Kösal, H. H., & Tosun, M. (2013). Split Fibonacci quaternions. Advances in Applied Clifford Algebras, 23(3), 535-545.
- Akyig̃it, M., Kösal, H. H., & Tosun, M. (2014). Fibonacci generalized quaternions. Advances in Applied Clifford Algebras, 24(3), 631-641.
- Aydın, F. T. (2021). Pauli–Fibonacci quaternions. Notes on Number Theory and Discrete Mathematics, 27(3), 184-193.
- Bilgici, G., Tokeşer, Ü. & Ünal, Z. (2017). k-Fibonacci and k-Lucas generalized quaternıons. Konuralp Journal of Mathematics, 5(2), 102-113
- Flaut, C., & Savin, D. (2015). Quaternion algebras and generalized Fibonacci–Lucas quaternions. Advances in Applied Clifford Algebras, 25(4), 853-862.
- Halici, S. (2012). On Fibonacci quaternions. Advances in Applied Clifford Algebras, 22(2), 321-327.
- Halici, S., & Karataş, A. (2017). On a generalization for Fibonacci quaternions. Chaos, Solitons & Fractals, 98, 178-182.
- Horadam, A. F. (1963). Complex Fibonacci numbers and Fibonacci quaternions. The American Mathematical Monthly, 70(3), 289-291.
- Iyer, M. R. (1969). A note on Fibonacci quaternions. Fibonacci Quart, 7(3), 225-229.
- Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Canada.
- Nurkan, S. K., & Güven, İ. A. (2015). Dual Fibonacci quaternions. Advances in Applied Clifford Algebras, 25(2), 403-414.
- Polatlı, E., Kızılates, C., & Kesim, S. (2016). On split k-Fibonacci and k-Lucas quaternions. Advances in Applied Clifford Algebras, 26(1), 353-362.
- Ramírez, J. L. (2015). Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions. Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, 23(2), 201-212.
- Şentürk, T. D., & Ünal, Z. (2022). 3-parameter generalized quaternions. Computational Methods and Function Theory, 1-34.
- Tan, E., Yilmaz, S., & Sahin, M. (2016). On a new generalization of Fibonacci quaternions. Chaos, Solitons & Fractals, 82, 1-4.
- Yüce, S., & Aydın, F. T. (2016). Generalized dual Fibonacci quaternions. Applied Mathematics E-Notes, 16(30), 276-289.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | November 30, 2022 |
| Published in Issue | Year 2022 |