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On the Location of Zeros of Polynomials
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American Journal of Computational Mathematics·Volume 01 (2011)·Pages 1–10·Published 30 March 2011·DOI10.4236/ajcm.2011.11001
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Abstract
In this paper, we prove some extensions and generalizations of the classical Eneström-Kakeya theorem.
KeywordsPolynomialZerosEneström-Kakeya Theorem
- A. Aziz and Q. G. Mohammad, “Zero-free Regions for Polynomials and Some Generalizations of Enestrom-Kakeya Theorem,” Canadian Mathematical Bulletin, Vol.27, 1984, pp. 265-272.
- 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, 1980, pp. 495-502. doi:10.1016/0022-247X(80)90097-9
- A. Aziz and B. A. Zargar, “Some Extensions of Enestrom – Kakeya Theorem,” Glasnik Matematicki, Vol. 31, 1996, p.51.
- G.T.Cargo and O. Shisha, “Zeros of Polynomials and Fractional Differences of Their Coefficients,” Journal of Mathematical Analysis and Applications, Vol.7, 1963, pp. 176-182. doi:10.1016/0022-247X(63)90046-5
- K. Dilcher, “A Generalization of the Enestrom-Kakeya theorem,” Journal of Mathematical Analysis and Applications, Vol. 116, 1986, pp. 473-488. doi:10.1016/S0022-247X(86)80012-9
- K. K. Dewan and M. Bidkham, “On the Enestrom – Kakeya Theorem,” Journal of Mathematical Analysis and Applications, Vol.180, 1993, pp. 29-36. doi:10.1006/jmaa.1993.1379
- N. K. Govil and V. K. Jain, “On the Enestrom – Kakeya Theorem II,” Journal of Approximation Theory, Vol. 22, 1978, pp. 1-10. doi:10.1016/0021-9045(78)90066-7
- N. K. Govil and Q. I. Rahman, “On the Enestrom-Kakeya Theorem,” Tohoku Ma-thematical Journal, Vol.20, 1968, pp. 126-136. doi:10.2748/tmj/1178243172
- A. Joyal, G. Labelle and Q. I. Rahman, “On the Location of Zeros of Polynomials,” Canadian Mathematical Bulletin, Vol. 10, 1967, pp. 53-63. doi:10.4153/CMB-1967-006-3
- P. V. Krishnaih, “On Kakeya Theorem” Journal of the London Mathematical Society, Vol. 30, 1955, pp. 314-319. doi:10.1112/jlms/s1-30.3.314
- M. Marden, “Geometry of Polynomials,” 2nd Edition, American Mathematical Society, Providence, 1966.
- Q. I. Rahman and G. Schmeisser, “Analytic Theory of Polynomials,” Oxford University Press, Oxford, 2002.
- T. Sheil-Small, “Complex Polynomials,” Cambridge University Press, Cambridge, 2002. doi:10.1017/CBO9780511543074
- W. M. Shah and A. Liman, “On the Zeros of a Certain Class of Polynomials and Related Analytic Functions,” Mathematicka Balkanicka, New Series, Vol. 19, No. 3-4, 2005, pp. 245-253.
- W. M. Shah, A. Liman and Shamim Ahmad Bhat, “On the Enestrom-Kakeya Theorem,” International Journal of Mathematical Science, Vol. 7, No. 1-2, 2008, pp. 111-120.