Bounds for the Zeros of a Polynomial with Restricted Coefficients

ABSTRACT

In this paper we shall obtain some interesting extensions and generalizations of a well-known theorem due to Enestrom and Kakeya according to which all the zeros of a polynomial P(Z =α_{n}Z^{n}+...+α_{1}Z+α_{0}satisfying the restriction α_{n}≥α_{n-1}≥...≥α_{1}≥α_{0}≥0 lie in the closed unit disk.

In this paper we shall obtain some interesting extensions and generalizations of a well-known theorem due to Enestrom and Kakeya according to which all the zeros of a polynomial P(Z =α

Cite this paper

A. Aziz and B. Zargar, "Bounds for the Zeros of a Polynomial with Restricted Coefficients,"*Applied Mathematics*, Vol. 3 No. 1, 2012, pp. 30-33. doi: 10.4236/am.2012.31005.

A. Aziz and B. Zargar, "Bounds for the Zeros of a Polynomial with Restricted Coefficients,"

References

[1] P. V. Krishnalah, “On Kakeya Theorem,” Journal of London Mathematical Society, Vol.20, No. 3, 1955, pp. 314- 319. doi:10.1112/jlms/s1-30.3.314

[2] A. Aziz and Q. G. Mohammad, “On the Zeros of a Certain Class of Polynomials and Related Analytic Functions,” Journal of Mathematical Analysis and Applications, Vol. 75, No. 2, 1980, pp. 495-502. doi:10.1016/0022-247X(80)90097-9

[3] N. K. Govil and Q. I. Rahman, “On the Enestrom-Kakeya Theorem II,” Tohoku Mathematical Journal, Vol. 20, No. 2, 1968, pp. 126-136. doi:10.2748/tmj/1178243172

[4] M. Marden, “Geometry of Polynomials,” 2nd Edition, Vol. 3, American Mathematical Society, Providence, 1966.

[5] G. VMilovanovic, D. S. Mitrovic and Th. M. Rassias, “Topics in Polynomials, Extremal Problems Inequalities, Zeros,” World Scientific, Singapore, 1994.

[6] A. Joyal, G. Labelle and Q. I. Rahman, “On the Location of Zeros of Polynomial,” Canadian Mathematical Bulletin, Vol. 10, 1967, pp. 53-63. doi:10.4153/CMB-1967-006-3

[7] A. Aziz and B. A. Zargar, “Some Extensions of Enestrom Kakeya Theorem,” Glasnick Matematicki, Vol. 31, 1996, pp. 239-244.

[8] K. K. Dewan and M. Bidkham, “On the Enestrom Kakeya Theorem,” Journal of Mathematical Analysis and Applications, Vol. 180, No. 1, 1993, pp. 29-36. doi:10.1006/jmaa.1993.1379

[1] P. V. Krishnalah, “On Kakeya Theorem,” Journal of London Mathematical Society, Vol.20, No. 3, 1955, pp. 314- 319. doi:10.1112/jlms/s1-30.3.314

[2] A. Aziz and Q. G. Mohammad, “On the Zeros of a Certain Class of Polynomials and Related Analytic Functions,” Journal of Mathematical Analysis and Applications, Vol. 75, No. 2, 1980, pp. 495-502. doi:10.1016/0022-247X(80)90097-9

[3] N. K. Govil and Q. I. Rahman, “On the Enestrom-Kakeya Theorem II,” Tohoku Mathematical Journal, Vol. 20, No. 2, 1968, pp. 126-136. doi:10.2748/tmj/1178243172

[4] M. Marden, “Geometry of Polynomials,” 2nd Edition, Vol. 3, American Mathematical Society, Providence, 1966.

[5] G. VMilovanovic, D. S. Mitrovic and Th. M. Rassias, “Topics in Polynomials, Extremal Problems Inequalities, Zeros,” World Scientific, Singapore, 1994.

[6] A. Joyal, G. Labelle and Q. I. Rahman, “On the Location of Zeros of Polynomial,” Canadian Mathematical Bulletin, Vol. 10, 1967, pp. 53-63. doi:10.4153/CMB-1967-006-3

[7] A. Aziz and B. A. Zargar, “Some Extensions of Enestrom Kakeya Theorem,” Glasnick Matematicki, Vol. 31, 1996, pp. 239-244.

[8] K. K. Dewan and M. Bidkham, “On the Enestrom Kakeya Theorem,” Journal of Mathematical Analysis and Applications, Vol. 180, No. 1, 1993, pp. 29-36. doi:10.1006/jmaa.1993.1379