[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2015.55.4.807

On Zeros of Polynomials with Restricted Coefficients

RASOOL, TAWHEEDA (Department of Mathematics, National Institute of Technology)
AHMAD, IRSHAD (Department of Mathematics, National Institute of Technology)
LIMAN, AB (Department of Mathematics, National Institute of Technology)

Publication Information

Kyungpook Mathematical Journal / v.55, no.4, 2015 , pp. 807-816 More about this Journal

Abstract

Let $P(z)={\limits\sum_{j=0}^{n}}a_jz^j$ be a polynomial of degree n and Re $a_j={\alpha}_j$ , Im $a_j=B_j$ . In this paper, we have obtained a zero-free region for polynomials in terms of ${\alpha}_j$ and ${\beta}_j$ and also obtain the bound for number of zeros that can lie in a prescribed region.

Keywords

Ploynomials; Zeros; $Enestr{\ddot{o}}om$ -Kakeya theroem;

Citations & Related Records

Reference

1	G. Enestrom, Remarquee sur un Theorem relative aux racinnes de I'equation $a_{n}z^{n}+a_{n-1}z^{n-1}+...a_{1}+a_{0}$ ou to us les coefficients sonts reels et possitifs, Tohoku Math. J., 18(1920), 34-36.
2	M. Marden, The Geometry of polynomials, Amer. Math. Monthly, 83(10)(1997), 788-797. DOI
3	Q. G. Mohammad, On the zeros of the polynomials, Amer. Math. Monthly, 72(6)(1965), 631-633. DOI
4	S. Kakeya, On the limits of the roots of an algebraic equation with positive coefficients, Tohoku Math. J., 2(1912-13), 140-142.
5	E. C. Titchmarsh, The theory of functions, 2nd ed. Oxford Univ. Press, London, (1939).