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A contraction of the Lucas polygon
Author(s):
Branko
Curgus;
Vania
Mascioni
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2973-2981.
MSC (2000):
Primary 30C15;
Secondary 26C10
Posted:
May 20, 2004
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Abstract:
The celebrated Gauss-Lucas theorem states that all the roots of the derivative of a complex non-constant polynomial  lie in the convex hull of the roots of  , called the Lucas polygon of  . We improve the Gauss-Lucas theorem by proving that all the nontrivial roots of  lie in a smaller convex polygon which is obtained by a strict contraction of the Lucas polygon of  .
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Additional Information:
Branko
Curgus
Affiliation:
Department of Mathematics, Western Washington University, Bellingham, Washington 98225
Email:
curgus@cc.wwu.edu
Vania
Mascioni
Affiliation:
Department of Mathematical Sciences, Ball State University, Muncie, Indiana 47306-0490
Email:
vdm@bsu-cs.bsu.edu
DOI:
10.1090/S0002-9939-04-07231-4
PII:
S 0002-9939(04)07231-4
Keywords:
Roots of polynomials,
critical points of polynomials,
Gauss-Lucas theorem
Received by editor(s):
October 29, 2002
Received by editor(s) in revised form:
February 12, 2003
Posted:
May 20, 2004
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2004,
American Mathematical Society
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