Bihyperbolic numbers of the Fibonacci type and their idempotent representation

Dorota Bród; Anetta Szynal-Liana; Iwona Włoch

Commentationes Mathematicae Universitatis Carolinae (2021)

  • Volume: 62, Issue: 4, page 409-416
  • ISSN: 0010-2628

Abstract

top
In this paper we introduce bihyperbolic numbers of the Fibonacci type. We present some of their properties using matrix generators and idempotent representations.

How to cite

top

Bród, Dorota, Szynal-Liana, Anetta, and Włoch, Iwona. "Bihyperbolic numbers of the Fibonacci type and their idempotent representation." Commentationes Mathematicae Universitatis Carolinae 62.4 (2021): 409-416. <http://eudml.org/doc/297547>.

@article{Bród2021,
abstract = {In this paper we introduce bihyperbolic numbers of the Fibonacci type. We present some of their properties using matrix generators and idempotent representations.},
author = {Bród, Dorota, Szynal-Liana, Anetta, Włoch, Iwona},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {hyperbolic number; bihyperbolic number; Fibonacci number; Pell number; Jacobsthal number},
language = {eng},
number = {4},
pages = {409-416},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Bihyperbolic numbers of the Fibonacci type and their idempotent representation},
url = {http://eudml.org/doc/297547},
volume = {62},
year = {2021},
}

TY - JOUR
AU - Bród, Dorota
AU - Szynal-Liana, Anetta
AU - Włoch, Iwona
TI - Bihyperbolic numbers of the Fibonacci type and their idempotent representation
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62
IS - 4
SP - 409
EP - 416
AB - In this paper we introduce bihyperbolic numbers of the Fibonacci type. We present some of their properties using matrix generators and idempotent representations.
LA - eng
KW - hyperbolic number; bihyperbolic number; Fibonacci number; Pell number; Jacobsthal number
UR - http://eudml.org/doc/297547
ER -

References

top
  1. Aydin F. T., 10.33434/cams.439752, Communications in Advanced Mathematical Sciences 1 (2018), no. 2, 142–155. DOI10.33434/cams.439752
  2. Bilgin M., Ersoy S., 10.1007/s00006-019-1036-2, Adv. Appl. Clifford Algebr. 30 (2020), no. 1, Paper No. 13, 17 pages. MR4054825DOI10.1007/s00006-019-1036-2
  3. Bród D., Szynal-Liana A., Włoch I., 10.1002/mma.7054, Math. Methods Appl. Sci. 44 (2021), no. 6, 4607–4615. MR4235524DOI10.1002/mma.7054
  4. Çimen C. B..Ipek A., 10.1007/s00006-015-0571-8, Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 39–51. MR3459988DOI10.1007/s00006-015-0571-8
  5. Halici S., 10.1007/s00006-011-0317-1, Adv. Appl. Clifford Algebr. 22 (2012), no. 2, 321–327. MR2930698DOI10.1007/s00006-011-0317-1
  6. Horadam A. F., 10.2307/2313129, Amer. Math. Monthly 70 (1963), 289–291. MR0146137DOI10.2307/2313129
  7. Iyer M. R., A note on Fibonacci quaternions, Fibonacci Quart. 7 (1969), no. 3, 225–229. MR0255513
  8. Nurkan S. K., Güven .I. A., A note on bicomplex Fibonacci and Lucas numbers, Int. J. Pure Appl. Math. 120 (2018), no. 3, 365–377. 
  9. Pogorui A. A., Rodríguez-Dagnino R. M., Rodríguez-Said R. D., 10.1080/17476930801973014, Complex Var. Elliptic Equ. 53 (2008), no. 7, 685–690. MR2431350DOI10.1080/17476930801973014
  10. Rochon D., Shapiro M., On algebraic properties of bicomplex and hyperbolic numbers, An. Univ. Oradea Fasc. Mat. 11 (2004), 71–110. MR2127591
  11. Sobczyk G., 10.1080/07468342.1995.11973712, The College Mathematics Journal 26 (1995), no. 4, 268–280. DOI10.1080/07468342.1995.11973712
  12. Szynal-Liana A., Włoch I., 10.1007/s00006-015-0622-1, Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 441–447. MR3460010DOI10.1007/s00006-015-0622-1
  13. Szynal-Liana A., Włoch I., 10.1007/s00006-015-0570-9, Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 435–440. MR3460009DOI10.1007/s00006-015-0570-9
  14. Szynal-Liana A., Włoch I., On Pell and Pell–Lucas hybrid numbers, Comment. Math. 58 (2018), no. 1–2, 11–17. MR3904772
  15. Szynal-Liana A., Włoch I., Hypercomplex Numbers of the Fibonacci Type, Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów, 2019. 
  16. Szynal-Liana A., Włoch I., On Jacobsthal and Jacobsthal–Lucas hybrid numbers, Ann. Math. Sil. 33 (2019), no. 1, 276–283. MR3982598
  17. Szynal-Liana A., Włoch I., The Fibonacci hybrid numbers, Util. Math. 110 (2019), 3–10. MR3967948

NotesEmbed ?

top

You must be logged in to post comments.