On the recursive sequence $x_{n+1}=\frac {A}{x_n}+\frac {1}{x_{n-2}}$
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- by R. DeVault, G. Ladas and S. W. Schultz
- Proc. Amer. Math. Soc. 126 (1998), 3257-3261
- DOI: https://doi.org/10.1090/S0002-9939-98-04626-7
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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.References
- G. Ladas, Open Problems and Conjectures, Journal of Difference Equations and Applications 2 (1996), 449-452.
- Ch. G. Philos, I. K. Purnaras, and Y. G. Sficas, Global attractivity in a nonlinear difference equation, Appl. Math. Comput. 62 (1994), no. 2-3, 249–258. MR 1284547, DOI 10.1016/0096-3003(94)90086-8
Bibliographic 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
- Received by editor(s): March 18, 1997
- Communicated by: Hal L. Smith
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3257-3261
- MSC (1991): Primary 39A10
- DOI: https://doi.org/10.1090/S0002-9939-98-04626-7
- MathSciNet review: 1473661