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

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 \[ x_{n+1} = \frac {A}{x_{n}} + \frac {1}{x_{n-2}}, \hspace {.2in} n = 0, 1, \ldots , \] 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

G. Ladas
Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881

S. W. Schultz
Affiliation: Department of Mathematics and Computer Science, Providence College, Providence, Rhode Island 02918

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