Geodesic
A generalization of the Gauss-Lucas theorem
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 481-486.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.
Classification : 12D10, 26C05, 30C15
Keywords: polynomials; location of zeros; convex hull of the zeros; Gauss-Lucas theorem 
@article{CMJ_2008__58_2_a12,
     author = {D{\'\i}az-Barrero, J. L. and Egozcue, J. J.},
     title = {A generalization of the {Gauss-Lucas} theorem},
     journal = {Czechoslovak Mathematical Journal},
     pages = {481--486},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {2008},
     mrnumber = {2411103},
     zbl = {1174.12001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008__58_2_a12/}
}
TY  - JOUR
AU  - Díaz-Barrero, J. L.
AU  - Egozcue, J. J.
TI  - A generalization of the Gauss-Lucas theorem
JO  - Czechoslovak Mathematical Journal
PY  - 2008
SP  - 481
EP  - 486
VL  - 58
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2008__58_2_a12/
LA  - en
ID  - CMJ_2008__58_2_a12
ER  - 
%0 Journal Article
%A Díaz-Barrero, J. L.
%A Egozcue, J. J.
%T A generalization of the Gauss-Lucas theorem
%J Czechoslovak Mathematical Journal
%D 2008
%P 481-486
%V 58
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2008__58_2_a12/
%G en
%F CMJ_2008__58_2_a12
Díaz-Barrero, J. L.; Egozcue, J. J. A generalization of the Gauss-Lucas theorem. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 481-486. http://geodesic.mathdoc.fr/item/CMJ_2008__58_2_a12/