Some Remarks on the Zeros of Tribonacci Polynomials

Oztunc Kaymak, Oznur

doi:10.28924/2291-8639-16-2018-368

Research Article

Some Remarks on the Zeros of Tribonacci Polynomials

Oznur Oztunc Kaymak¹

Balıkesir University

Abstract

In this paper, the zeros of Tribonacci polynomials are studied. The bound containing the zeros of Tribonacci polynomials has been numerically examined with comparisons. On the other hand, a new algorithm is given so that it can be used in other boundary problems.

How to Cite

O. Oztunc Kaymak, Some Remarks on the Zeros of Tribonacci Polynomials, Int. J. Anal. Appl. 16 (2018), 368–373. https://doi.org/10.28924/2291-8639-16-2018-368

BibTeX

@article{Kaymak2018,
  author  = {Oztunc Kaymak, Oznur},
  title   = {Some Remarks on the Zeros of Tribonacci Polynomials},
  journal = {Int. J. Anal. Appl.},
  volume  = {16},
  year    = {2018},
  pages   = {368--373},
  doi     = {10.28924/2291-8639-16-2018-368}
}

References

[1] A. L. Cauchy, Exercises de Mathématiques IV, Anné de Bure Fréres, Paris, 1829.
[2] G. Moore, The limit of the golden numbers is 3/2, Fibonacci Quart. 32 (1994), 211-217.
[3] M. X. He, D. Simon, P. E. Ricci, Dynamics of the zeros of Fibonacci polynomials, Fibonacci Quart. 35 (1997), 160-168.
[4] A. Dalal, N. K. Govil, On Region Containing all the Zeros of a Polynomial, Appl. Math. Comput. 219 (2013), 9609-9614.
[5] T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, 2001.
[6] V. E. Hoggat, M. Bicknell, Generalized Fibonacci polynomials, Fibonacci Quart. 11 (1973), 457-465.
[7] V. E. Hoggat, M. Bicknell, Roots of Fibonacci polynomials, Fibonacci Quart. 11 (1973), 271-274.
[8] F. Matyas, Bounds for the zeros of Fibonacci-Like Polynomials, Acta Acad. Paed. Agriensis, Sec. Math. 25 (1998), 15-20.
[9] H. Prodinger, The asymptotic behavior of the golden numbers, Fibonacci Quart. 34 (1996), 224-225.
[10] J. H. Conway, R. Guy, The Book of Numbers, Copernicus, New York, 1996.
[11] W. Goh, M. X. He, P. E. Ricci, On the universal zero attractor of the Tribonacci-related polynomials, Calcolo 46 (2009), 95-129.
[12] M. X. He, P. E. Ricci, D. Simon, Numerical results on the zeros of generalized Fibonacci polynomials, Calcolo 34 (1997), 25-40.
[13] J.L. Diaz-Barrero, An annulus for the zeros of polynomials, J. Math. Anal. Appl. 273 (2002), 349-352.
[14]Ö.Öztun ¸c, R-Bonacci Polynomials and Their Derivatives, Ph. D. Thesis, Balikesir University, (2014).
[15] X. Li, Y. Shi, I. Gutman, Graph Energy, Springer, New York, 2012.
[16] S. Fisk, Polynomials, roots, and interlacing, ArXiv mat/0612833v2, (2006).
[17] N. Y.Özgür,Ö.Öztun ¸c, On the Zeros of R-Bonaci Polynomials, ArXiv:1711.01150, (2017).
[18] P. G. Anderson, R. S. Gaborski, The Polynomial Method Augmented by Supervised Training for Hand-Printed Character Recognition, Artificial Neural Networks and Genetic Algorithms, Proceedings of the International Conference, (1993).
[19] S. Ucar, N. Y. Ozgur, Right Circulant Matrices with Generalized Fibonacci and Lucas Polynomials and Coding Theory, ArXiv:1801.01766 [math.CO].