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.

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.

nullG. Singh and W. Shah, "On The Eneström-Kakeya Theorem,"

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.

[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.