On the Robustness property of Eneström-Kakeya theorem
- Authors
- Choo, Y.; Choi, G.K.
- Issue Date
- 2011
- Keywords
- Eneström-Kakeya theorem; Polynomial; Zero
- Citation
- International Journal of Mathematical Analysis, v.5, no.41-44, pp.2089 - 2096
- Journal Title
- International Journal of Mathematical Analysis
- Volume
- 5
- Number
- 41-44
- Start Page
- 2089
- End Page
- 2096
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/20587
- ISSN
- 1312-8876
- Abstract
- The Eneström-Kakeya theorem states that an nth-order polynomial P(z) = ∑ n i=0 a iz i with positive coefficients has all its zeros in the disk |z| ≤ 1 if its coefficients monotonically decrease, i.e., a n ≥ a n-1 ≥...≥ a 1 ≥ a 0 > 0. In the literature some attempts have been made to extend and generalize the Eneström-Kakeya theorem. In this paper we study the robustness property of the Eneström-Kakeya theorem. It is shown that even if the monotonicity is violated by one coefficient (say a k), then all the zeros of P(z) still remain in the disk |z| ≤ 1 if the deviation of ak from a k+1 or a k-1 is not too large. More precisely we derive the upper bounds for the deviations of a k from a k+1 or a k-1 to ensure that P(z) has all its zeros in the disk |z| ≤ 1.
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Collections - College of Science and Technology > Department of Electronic and Electrical Engineering > 1. Journal Articles
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