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Zero-Free Regions for Polynomials and Some Generalizations of Eneström-Kakeya Theorem

Published online by Cambridge University Press:  20 November 2018

Abdul Aziz  and
Q. G. Mohammad
Abdul Aziz
Affiliation:
Post-Graduate Department of Mathematics, University of Kashmir, Hazratbal Srinagar-190006 Kashmir, India
Q. G. Mohammad
Affiliation:
Post-Graduate Department of Mathematics, University of Kashmir, Hazratbal Srinagar-190006 Kashmir, India
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Abstract

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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.

Keywords

30A0430A0630A4041A10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 265 - 272
Copyright
Copyright © Canadian Mathematical Society 1984

References

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. 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. Gershgorin, G., Über die Abgrenzung der Eigenwerte einer Matrix, Izv. Akad. Nauk SSSR, 7 (1931), 749–754.Google Scholar
4. Govil, N. K. and Rahman, Q. I., On the Enestrom-Kakeya theorem, Tôhôku Math. J. 20 (1968), 126–136.Google Scholar
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. Krishnaiah, P. V., On Kakeya theorem, J. London Math. Soc. 30 (1955), 314–319.Google Scholar
7. Mohammad, Q. G., Location of the zeros of polynomials, Amer. Math. Monthly 74 (1967), 290–292.Google Scholar
8. Marden, M., Geometry of Polynomials, Math. Surveys No. 3, Amer. Math. Soc, Providence, R.I., 1966.Google Scholar
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. Taussky, O., A recurring theorem in determinants, Amer. Math. Monthly 56 (1949), 672–676.Google Scholar