Geodesic
Zero-Free Regions for Polynomials and Some Generalizations of Eneström-Kakeya Theorem
Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 265-272

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we shall use matrix methods to obtain several generalizations of a well known result of Eneström and Kakeya about the location of the zeros of polynomials. We shall also obtain zero-free regions of polynomials having complex coefficients. Finally we prove some results concerning the zeros of a class of polynomials.
DOI : 10.4153/CMB-1984-040-3
Mots-clés : 30A04, 30A06, 30A40, 41A10 
Aziz, Abdul; Mohammad, Q. G. Zero-Free Regions for Polynomials and Some Generalizations of Eneström-Kakeya Theorem. Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 265-272. doi: 10.4153/CMB-1984-040-3
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[1] 1. Aziz, Abdul and Mohammad, Q. G., On the zeros of a certain class of polynomials and related analytic functions, J. Math. Anal. Appl. 75 (1980), 495–502. Google Scholar

[2] 2. Cargo, G. T. and Shisha, O., Zeros of polynomials and fractional order differences of their coefficients, J. Math. Anal. Appl. 7 (1963), 176–182. Google Scholar

[3] 3. Gershgorin, G., Über die Abgrenzung der Eigenwerte einer Matrix, Izv. Akad. Nauk SSSR, 7 (1931), 749–754. Google Scholar

[4] 4. Govil, N. K. and Rahman, Q. I., On the Enestrom-Kakeya theorem, Tôhôku Math. J. 20 (1968), 126–136. Google Scholar

[5] 5. Joyal, A., Labelle, G. and Rahman, Q. I., On the location of zeros of polynomials, Canad. Math. Bull. 10 (1967), 53–63. Google Scholar

[6] 6. Krishnaiah, P. V., On Kakeya theorem, J. London Math. Soc. 30 (1955), 314–319. Google Scholar

[7] 7. Mohammad, Q. G., Location of the zeros of polynomials, Amer. Math. Monthly 74 (1967), 290–292. Google Scholar

[8] 8. Marden, M., Geometry of Polynomials, Math. Surveys No. 3, Amer. Math. Soc, Providence, R.I., 1966. Google Scholar

[9] 9. Schaeffer, A. C., Inequalities of A. Markoff and S. Bernstein for polynomials and related functions, Bull. Amer. Math. Soc. 47 (1941), 565–579. Google Scholar

[10] 10. Taussky, O., A recurring theorem in determinants, Amer. Math. Monthly 56 (1949), 672–676. Google Scholar

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