On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem

Botta, V. and Meneguette, M. and Cuminato, J. A. and McKee, S. (2012) On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem. Journal of Mathematical Analysis and Applications, 385 (2). pp. 1151-1161. ISSN 0022-247X (https://doi.org/10.1016/j.jmaa.2011.07.037)

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Abstract

This paper presents an extension of the Eneström–Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K,L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994).

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