AM  Vol.1 No.6 , December 2010
On The Eneström-Kakeya Theorem
ABSTRACT
In this paper, we prove some generalizations of results concerning the Eneström-Kakeya theorem. The results obtained considerably improve the bounds by relaxing the hypothesis in some cases.

Cite this paper
nullG. Singh and W. Shah, "On The Eneström-Kakeya Theorem," Applied Mathematics, Vol. 1 No. 6, 2010, pp. 555-560. doi: 10.4236/am.2010.16073.
References
[1]   M. Marden, “Geometry of Polynomials,” 2nd Edition, American Mathematical Society, Providence, 1966.

[2]   E. Egervary, “On a Generalization of a Theorem of Kakeya, ” Acta Mathematica Scientia, Vol. 5, 1931, pp. 78-82.

[3]   N. K. Govil and Q. I. Rahman, “On the Enestr?m-Kakeya Theorem II,” Tohoku Mathematical Journal, Vol. 20, 1968, pp. 126-136.

[4]   W. M. Shah and A. Liman, “On the Zeros of a Certain Class of Polynomials and Related Analytic Functions,” Mathe- maticka Balkanicka, New Series, Vol. 19, No. 3-4, 2005, pp. 245-253.

[5]   W. M. Shah, A. Liman and Shamim Ahmad Bhat, “On the Enestr?m-Kakeya Theorem,” International Journal of Mathematical Science, Vol.7, No. 1-2, 2008, pp. 111-120.

[6]   G. V. Milovanovic, D. S. Mitrinovic and Th. M. Rassias, “Topics in Polynomials, Extremal Properties, Inequalities and Zeros,” World Scientific Publishing Company, Singapore, 1994.

[7]   Q. I. Rahman and G. Schmeisser, “Analytic Theory of Polynomials,” Oxford University Press, Oxford, 2002.

[8]   T. Sheil-Small, “Complex Polynomials,” Cambridge University Press, Cambridge, 2002.

[9]   Joyal, G. Labelle and Q. I. Rahman, “On the Location of Zeros of Polynomials,” [9] Joyal, G. Labelle and Q. I. Rahman, “On the Location of Zeros of Polynomials,” Canadian Mathematical Bulletion, Vol. 10, 1967, pp. 53-63.. Vol. 10, 1967, pp. 53-63.

[10]   K. K. Dewan and M. Bidkham, “On the Enestr?m- Kakeya Theorem,” Journal of Mathematical Analysis and Applications Vol. 180, 1993, pp. 29-36.

[11]   A. Aziz and Q. G. Mohammad, “Zero-free Regions for Polynomials and Some Generalizations of Enestrom- Kakeya Theorem,” [9] Joyal, G. Labelle and Q. I. Rahman, “On the Location of Zeros of Polynomials,” Canadian Mathematical Bulletion, Vol. 10, 1967, pp. 53-63. Vol. 27, 1984, pp. 265-272.

[12]   A. Aziz and B. A. Zargar, “Some Extensions of Enestr?m- Kakeya Theorem,” Glasnik Matematicki, Vol. 31, 1996, pp. 239-244.

 
 
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