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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the recursive sequence ${\displaystyle}x_{n+1}=\frac A{x_n}+\frac 1{x_{n-2}}$


Authors: R. DeVault, G. Ladas and S. W. Schultz
Journal: Proc. Amer. Math. Soc. 126 (1998), 3257-3261
MSC (1991): Primary 39A10
MathSciNet review: 1473661
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Abstract: We show that every positive solution of the equation

\begin{displaymath}x_{n+1} = \frac{A}{x_{n}} + \frac{1}{x_{n-2}}, \hspace{.2in} n = 0, 1, \ldots , \end{displaymath}

where $ A \in (0, \infty)$, converges to a period two solution.


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Additional Information

R. DeVault
Affiliation: Division of Mathematics and Sciences, Northwestern State University, Natchitoches, Louisiana 71497
Email: rich@alpha.nsula.edu

G. Ladas
Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881
Email: gladas@math.uri.edu

S. W. Schultz
Affiliation: Department of Mathematics and Computer Science, Providence College, Providence, Rhode Island 02918
Email: sschultz@providence.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04626-7
PII: S 0002-9939(98)04626-7
Keywords: Recursive sequence, global asymptotic stability, period two solution
Received by editor(s): March 18, 1997
Communicated by: Hal L. Smith
Article copyright: © Copyright 1998 American Mathematical Society