On the Robustness property of Eneström-Kakeya theorem
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Choo, Y. | - |
dc.contributor.author | Choi, G.K. | - |
dc.date.accessioned | 2021-12-15T04:44:05Z | - |
dc.date.available | 2021-12-15T04:44:05Z | - |
dc.date.created | 2021-12-10 | - |
dc.date.issued | 2011 | - |
dc.identifier.issn | 1312-8876 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/20587 | - |
dc.description.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. | - |
dc.language | 영어 | - |
dc.language.iso | en | - |
dc.title | On the Robustness property of Eneström-Kakeya theorem | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Choo, Y. | - |
dc.contributor.affiliatedAuthor | Choi, G.K. | - |
dc.identifier.scopusid | 2-s2.0-84856533327 | - |
dc.identifier.bibliographicCitation | International Journal of Mathematical Analysis, v.5, no.41-44, pp.2089 - 2096 | - |
dc.relation.isPartOf | International Journal of Mathematical Analysis | - |
dc.citation.title | International Journal of Mathematical Analysis | - |
dc.citation.volume | 5 | - |
dc.citation.number | 41-44 | - |
dc.citation.startPage | 2089 | - |
dc.citation.endPage | 2096 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scopus | - |
dc.subject.keywordAuthor | Eneström-Kakeya theorem | - |
dc.subject.keywordAuthor | Polynomial | - |
dc.subject.keywordAuthor | Zero | - |
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