American Journal of Mathematical Analysis. 2014, 2(2), 23-27
DOI: 10.12691/ajma-2-2-2
Open AccessArticle
M S PUKHTA1,
1Division of Agri. Statistics, Sher-e-Kashmir, University of Agricultural Sciences and Technology of Kashmir, India
Pub. Date: May 25, 2014
Cite this paper:
M S PUKHTA. On Location of Zeros of Polynomials. American Journal of Mathematical Analysis. 2014; 2(2):23-27. doi: 10.12691/ajma-2-2-2
Abstract
If
be a polynomial of degree n such that aj=aj+ibj where aj and bj, j = 0, 1, ….., n are real numbers. In this paper we obtain a generalization of well known result of Eneström -Kakeya concerning the bounds for the moduli of the zeros of polynomials with complex coefficients which improve upon some results due to A. Aziz and Q.G Mohammad and others.Keywords:
complex polynomials zeros Eneström – Kakeya Theorem
This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit
http://creativecommons.org/licenses/by/4.0/
References:
[1] | A. Aziz and Q. G. Mohammad, Zero free regions for polynomials and some generalizations of Enström-Kakeya theorem, Cand. Math. Bull., 27(1984), 265-272. |
|
[2] | G. Eneström, Remarqueesur un The’ore’me’relatif aux racines de I’ equation anxn + an-1xn-1 + ……+ a0 = 0 outous les coefficients sont reels et possitifs, Tôhoku Math. J., 18 (1920), 34-36. |
|
[3] | A. Hurwitz, Űberdie Nullslenllen der Bessel Schen Function, Math. Ann., 33(1989)246-266. |
|
[4] | A.Joyal, G.Labelle and Q.I. Rahman, On the location of zeros of polynomials, Canad. Math. Bull., 10 (1967), 53-63. |
|
[5] | S.Kakeya, On the limits of the roots of an algebraic equation with positive coefficients, Tôhoku Math. J., 2 (1912-13), 140-142. |
|
[6] | A. Aziz and B. A. Zargar, Some extensions of Enström-Kakeya Theorem, Glasnik Mate., 31(1996), 239-244. |
|