Location of the critical points of certain polynomials
نویسندگان
چکیده
منابع مشابه
On the Location of Critical Points of Polynomials
Given a polynomial p of degree n ≥ 2 and with at least two distinct roots let Z(p) = {z : p(z) = 0}. For a fixed root α ∈ Z(p) we define the quantities ω(p, α) := min { |α − v| : v ∈ Z(p) \ {α} } and τ(p, α) := min { |α − v| : v ∈ Z(p′) \ {α} } . We also define ω(p) and τ(p) to be the corresponding minima of ω(p, α) and τ(p, α) as α runs over Z(p). Our main results show that the ratios τ(p, α)/...
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On the Location of the Zeros of Certain Polynomials
Abstract. We extend Aziz and Mohammad’s result that the zeros, of a polynomial P (z) = ∑n j=0 ajz , taj > aj−1 > 0, j = 2, 3, . . . , n for certain t ( > 0), with moduli greater than t(n − 1)/n are simple, to polynomials with complex coefficients. Then we improve their result that the polynomial P (z), of degree n, with complex coefficients, does not vanish in the disc |z − ae| < a/(2n); a > 0,...
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It is shown that a polynomial with a Cremer periodic point has a non-accessible critical point in its Julia set provided that the Cremer periodic point is approximated by small cycles. Stony Brook IMS Preprint #1995/2 February 1995
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ژورنال
عنوان ژورنال: Annales UMCS, Mathematica
سال: 2013
ISSN: 2083-7402,0365-1029
DOI: 10.2478/v10062-012-0025-x