Remarks on the Gauss-Lucas theorem in higher dimensional space-Reference-Cited by-同舟云学术

Remarks on the Gauss-Lucas theorem in higher dimensional space

Published:1976 Issue:1 Volume:55 Page:97-102
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Goodman A. W.

Abstract

A recent paper by J. B. Diaz and Dorothy Browne Shaffer extends the Gauss-Lucas Theorem to n n -dimensional Euclidean space. The authors leave open certain natural questions concerning the existence of “zeros of the derivative". This paper answers three such questions, and suggests several other questions for further investigation.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1976-055-01/S0002-9939-1976-0435366-6/S0002-9939-1976-0435366-6.pdf

Reference5 articles.

1. A generalization, to higher dimensions, of a theorem of Lucas concerning the zeros of the derivative of a polynomial of one complex variable;Díaz, J. B.;Applicable Anal.,1976

2. Pure and Applied Mathematics, Vol. 7;Dunford, Nelson,1958

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

4. Über die Lage der Nullstellen eines Abstandspolynoms und seiner Derivierten;v. Sz. Nagy, Gyula;Bull. Amer. Math. Soc.,1949

5. On the location of the zeros of the derivative of rational functions of distance polynomials;Schurrer, Augusta;Trans. Amer. Math. Soc.,1958

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