Annulus containing all the zeros of a polynomial
نویسندگان
چکیده
Recently Dalal and Govil [5] proved that, for any set of positive numbers {Ak}k=1 such that ∑n k=1 Ak = 1, a complex polynomial P (z) = ∑n k=0 dkz k (dk = 0, 0 ≤ k ≤ n) has all its zeros in the annulus A = {z : r1 ≤ |z| ≤ r2}, where r1 = min 1≤k≤n { Ak ∣∣∣d0 dk ∣∣∣ } 1 k and r2 = max 1≤k≤n { 1 Ak ∣∣∣dn−k dn ∣∣∣ } 1 k . This paper presents the best possible results in the same direction by identifying the smallest annulus containing all the zeros of P (z). Mathematics Subject Classification: 30C10, 30C15
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ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 249 شماره
صفحات -
تاریخ انتشار 2014