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On solutions of the recursive equations x_{n+1}=x_{n-1}^{p}/x_{n}^{p} (p>0) via Fibonacci-type sequences

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dc.contributor.author Öcalan, Özkan
dc.contributor.author Duman, Oktay
dc.date.accessioned 2019-12-25T14:34:16Z
dc.date.available 2019-12-25T14:34:16Z
dc.date.issued 2019-01
dc.identifier.citation Öcalan, Ö., & Duman, O. (2019). On solutions of the recursive equations x_{n+1}=x_{n-1}^{p}/x_{n}^{p} (p>0) via Fibonacci-type sequences. Electronic Journal of Mathematical Analysis and Applications, 7(1), 102-115. en_US
dc.identifier.issn 2090-729X
dc.identifier.uri https://tinyurl.com/tnwmnwd
dc.identifier.uri http://hdl.handle.net/20.500.11851/2943
dc.description.abstract Abstract. In this paper, by using the classical Fibonacci sequence and the golden ratio, we first give the exact solution of the nonlinear recursive equation xn+1 = xn−1/xn with respect to certain powers of the initial values x−1 and x0. Then we obtain a necessary and sufficient condition on the initial values for which the equation has a non-oscillatory solution. Later we extend our all results to the recursive equations xn+1 = xp n−1/xp n (p > 0) in a similar manner. We also get a characterization for unbounded positive solutions. At the end of the paper we analyze all possible positive solutions and display some graphical illustrations verifying our results. en_US
dc.language.iso eng en_US
dc.rights info:eu-repo/semantics/openAccess
dc.title On solutions of the recursive equations x_{n+1}=x_{n-1}^{p}/x_{n}^{p} (p>0) via Fibonacci-type sequences en_US
dc.type article en_US
dc.relation.journal Electronic Journal of Mathematical Analysis and Applications en_US
dc.contributor.department TOBB ETU, Faculty of Science and Literature, Depertment of Mathematics en_US
dc.contributor.department TOBB ETÜ, Fen Edebiyat Fakültesi, Matematik Bölümü tr_TR
dc.identifier.volume 7
dc.identifier.issue 1
dc.identifier.startpage 102
dc.identifier.endpage 115
dc.contributor.orcid http://orcid.org/0000-0001-7779-6877
dc.contributor.tobbetuauthor Duman, Oktay
dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı tr_TR


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