Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/2943
Title: On solutions of the recursive equations x_{n+1}=x_{n-1}^{p}/x_{n}^{p} (p>0) via Fibonacci-type sequences
Authors: Öcalan, Özkan
Duman, Oktay
Issue Date: Jan-2019
Source: 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.
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.
URI: https://tinyurl.com/tnwmnwd
https://hdl.handle.net/20.500.11851/2943
ISSN: 2090-729X
Appears in Collections:Matematik Bölümü / Department of Mathematics

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