A refinement of the Gauss-Lucas theorem-Reference-Cited by-同舟云学术

A refinement of the Gauss-Lucas theorem

Published:1998 Issue:7 Volume:126 Page:2065-2070
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Dimitrov Dimitar

Abstract

The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p p lie in the convex hull Ξ \Xi of the zeros of p p . It is proved that, actually, a subdomain of Ξ \Xi contains the critical points of p p .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1998-126-07/S0002-9939-98-04381-0/S0002-9939-98-04381-0.pdf

Reference5 articles.

1. F. Lucas, Propriétés géométriques des fractions rationnelles, C. R. Acad. Sci. Paris 77(1874), 431-433; 78(1874), 140-144; 78(1874), 180-183; 78(1874), 271-274.

2. Mathematical Surveys, No. 3;Marden, Morris,1966

3. Conjectures on the critical points of a polynomial;Marden, Morris;Amer. Math. Monthly,1983

4. G. Szegő, Bemerkungen zu einen Satz von J.H.Grace über die Wurzeln algebraischer Gleichungen, Math.Z. 13(1922), 28-55.

5. J. L. Walsh, On the location of the roots of the derivative of a polynomial, C. R. Congr. Internat. des Mathématiciens, Strasbourg, 1920, pp. 339-342.

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