An annulus for the zeros of polynomials

On annuli containing all the zeros of a polynomial

“…In case of Example 3, our Theorem 1.7 gives the sharpest bound. Our last example is the one considered in Diaz-Barrero [7] and we see that for the polynomial in this example, although the inner radius of the annulus obtained by Theorem 1.3 is slightly bigger, but in terms of area, our Theorem 1.8 again gives the sharpest bound.…”

“…Diaz-Barrero [7] gave another refinement of Theorem 1.1, by proving the following: Theorem 1.3. Let p(z) = n j=0 a j z j (a j = 0) be a non-constant complex polynomial.…”

Location of zeros of polynomials

“…Recently, Diaz-Barrero [2] has obtained bounds for zeros of polynomials in terms of binomial coefficients and Fibonacci numbers (F 0 D 0, F 1 D 1 and F nC1 D F n C F n 1 , n 1). Precisely he proved the following result.…”

Annular Bounds for the Zeros of a Polynomial

“…Diaz-Barrero [11] gave the following results, providing circular regions containing all the zeros of a polynomial in terms of the binomial coefficients and Fibonacci's numbers. Note that the binomial coefficients are defined by…”