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On a Problem Related to The Conjecture of Sendov About The Critical Points of a Polynomial

Published online by Cambridge University Press:  20 November 2018

Q. I. Rahman  and
Q. M. Tariq
Q. I. Rahman
Affiliation:
Département de Mathématiques et de Statistique Université de Montréal Montréal, PQ H3C 3J7
Q. M. Tariq
Affiliation:
Département de Mathématiques et de Statistique Université de Montréal Montréal, PQ H3C 3J7
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Abstract

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Let P be a polynomial of degree n having all its zeros in the closed unit disk. Given that a is a zero (of P) of multiplicity k we seek to determine the radius ρ(n; k; a) of the smallest disk centred at a containing at least k zeros of the derivative P'. In the case k = 1 the answer has been conjectured to be 1 and is known to be true for n ≦ 5. We prove that ρ(n; k; a) ≦ 2k/(k + 1) for arbitrary k ∊ N and n ≦ k + 4.

Keywords

30C15 (Primary)
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 476 - 480
Copyright
Copyright © Canadian Mathematical Society 1987

References

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