On the location of critical points of some complex polynomials

• Autorzy: Dronka J. , Sokół J.
• Języki publikacji: EN

Abstrakty

EN

Let P(a,n) be the set of all complex polynomials of degree n which have all their roots in the closed unit disk and one fixed root at a, 0 < a < 1. In this paper we show thiat for n > 3 all critical points of the polynomial f(z)= (zn-l+ l)(z - a) lie outside the set K(a,n) consisting of all b such that for some c the polynomial p(z)= (z - b) n - c belongs to P(a,n). Hence we infer that minimal sets satisfying the Sendov property (i.e. containing at least one critical point of each pzawiera P(a, n) ) exist but they are not unique.

Słowa kluczowe

EN

polynomials; zeros of the derivative; Sendov; minimal sets

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 1999
• Tom: Vol. 32, nr 2
• Strony: 297--302
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Dronka J.

autor

Sokół J.

• Department of Mathematics Technical University of Rzeszów