Generalized commutative quaternion polynomials of the Fibonacci type

Anetta Szynal-Liana, Iwona Włoch, Mirosław Liana

Abstract


Generalized commutative quaternions is a number system which generalizes elliptic, parabolic and hyperbolic quaternions, bicomplex numbers, complex hyperbolic numbers and hyperbolic complex numbers. In this paper we introduce and study generalized commutative quaternion polynomials of the Fibonacci type.

Keywords


Quaternions; generalized quaternions; polynomials; Fibonacci type numbers

Full Text:

PDF

References


Bród, D., Szynal-Liana, A., Włoch, I., On some combinatorial properties of generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal–Lucas quaternions, Czechoslovak Math. J. 72 (147) (2022), 1239–1248. https://doi.org/10.21136/CMJ.2022.0174-22

Danielewski, M., Sapa, L., Foundations of the quaternion quantum mechanics, Entropy 2020, 22 (12), 1424, 20 pp. https://doi.org/10.3390/e22121424

Hamilton, W. R., Lectures on Quaternions, Hodges and Smith, Dublin, 1853.

Horadam, A. F., Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly 70 (3) (1963), 289–291.

Horadam, A. F., Quaternion recurrence relations, Ulam Quat. 2 (2) (1993), 23–33.

Iakin, A. L., Generalized quaternions of higher order, Fibonacci Quart. 15 (4) (1977), 343–346.

Iakin, A. L., Generalized quaternions with quaternion components, Fibonacci Quart. 15 (4) (1977), 350–352.

Iyer, M. R., A note on Fibonacci quaternions, Fibonacci Quart. 7 (3) (1969), 225–229.

Jafari, M., Yayli, Y., Generalized quaternions and their algebraic properties, Commun. Fac. Sci. Univ. Ankara Ser. A1 Math. Stat. 64 (1) (2015), 15–27. https://doi.org/10.1501/Commua1_0000000724

Kızılates, C., On quaternions with incomplete Fibonacci and Lucas numbers components, Util. Math. 110 (2022), 263–269. https://utilitasmathematica.com/index.php/Index/article/view/1434

Kızılates, C., Catarino, P., Tuglu, N., On the bicomplex generalized Tribonacci quaternions, Mathematics 2019, 7 (1), 80, 8 pp. https://doi.org/10.3390/math7010080

Kızılates, C., Kone, T., On higher order Fibonacci hyper complex numbers, Chaos Solitons Fractals 148 (2021), 111044. https://doi.org/10.1016/j.chaos.2021.111044

Kızılates, C., Kone,T., On higher order Fibonacci quaternions, J. Anal. 29 (2021), 1071–1082. https://doi.org/10.1007/s41478-020-00295-1

Pei, S.-C., Chang, J.-H., Ding, J.-J., Commutative reduced biquaternions and their Fourier transform for signal and image processing applications, IEEE Transactions on Signal Processing 52 (7) (2004), 2012–2031. https://doi.org/10.1109/TSP.2004.828901

Pinotsis, D. A., Segre quaternions, spectral analysis and a four-dimensional Laplace equation, in: Progress in Analysis and its Applications, M. Ruzhansky, J. Wirth, eds., World Scientific, Singapore, 2010, 240–246. https://doi.org/10.1142/9789814313179_0032

Segre, C., Le Rappresentazioni Reali delle Forme Complesse a Gli Enti Iperalgebrici, Math. Ann. 40 (1892), 413–467.

Swamy, M. N. S., On generalized Fibonacci quaternions, Fibonacci Quart. 11 (5) (1973), 547–549.

Szynal-Liana, A., Włoch, I., Hypercomplex numbers of the Fibonacci type, Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów, 2019.

Szynal-Liana, A., Włoch, I., Generalized commutative quaternions of the Fibonacci type, Bol. Soc. Mat. Mex. 28 (2022), Art. No. 1, 9 pp. https://doi.org/10.1007/s40590-021-00386-4

Terzioglu, N., Kızılate¸s, C., Du, W.-S., New properties and identities for Fibonacci finite operator quaternions, Mathematics 2022, 10, 1719. https://doi.org/10.3390/math10101719

The On-Line Encyclopedia of Integer Sequences, http://oeis.org/

Tuglu, N., Kocer, E. G., Stakhov, A., Bivariate Fibonacci like p-polynomials, Appl. Math. Comput. 217 (24) (2011), 10239–10246. https://doi.org/10.1016/j.amc.2011.05.022




DOI: http://dx.doi.org/10.17951/a.2022.76.2.33-44
Date of publication: 2023-03-13 22:27:58
Date of submission: 2023-03-12 17:25:53


Statistics


Total abstract view - 697
Downloads (from 2020-06-17) - PDF - 412

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 Anetta Szynal-Liana, Iwona Włoch, Mirosław Liana