On the dynamics of a third order Newton's approximation method

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dc.citation.epage56en_US
dc.citation.issueNumber1en_US
dc.citation.spage50en_US
dc.citation.volumeNumber290en_US
dc.contributor.authorGheondea, A.en_US
dc.contributor.authorŞamcı, M. E.en_US
dc.date.accessioned2018-04-12T10:38:52Z
dc.date.available2018-04-12T10:38:52Z
dc.date.issued2017en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractWe provide an answer to a question raised by S. Amat, S. Busquier, S. Plaza on the qualitative analysis of the dynamics of a certain third order Newton type approximation function Mf, by proving that for functions f twice continuously differentiable and such that both f and its derivative do not have multiple roots, with at least four roots and infinite limits of opposite signs at ±∞, Mf has periodic points of any prime period and that the set of points a at which the approximation sequence (Mn f(a))n ∈ ℕ does not converge is uncountable. In addition, we observe that in their Scaling Theorem analyticity can be replaced with differentiability. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheimen_US
dc.identifier.doi10.1002/mana.201500470en_US
dc.identifier.eissn1522-2616
dc.identifier.issn0025-584X
dc.identifier.urihttp://hdl.handle.net/11693/36409
dc.language.isoEnglishen_US
dc.publisherWileyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1002/mana.201500470en_US
dc.source.titleMathematische Nachrichtenen_US
dc.subject37E15en_US
dc.subjectchaosen_US
dc.subjectNewton’s approximation methoden_US
dc.subjectperiodic pointsen_US
dc.subjectPrimary: 37N30en_US
dc.subjectSecondary: 37D45en_US
dc.subjectthird orderen_US
dc.titleOn the dynamics of a third order Newton's approximation methoden_US
dc.typeArticleen_US

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