Discrete Dynamics in Nature and Society

Volume 2009 (2009), Article ID 608976, 8 pages

http://dx.doi.org/10.1155/2009/608976

Research Article

## On the Recursive Sequence

College of Computer Science, Chongqing University, Chongqing 400044, China

Received 15 December 2008; Accepted 7 May 2009

Academic Editor: Guang Zhang

Copyright © 2009 Fangkuan Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Linked References

- A. M. Amleh, E. A. Grove, G. Ladas, and D. A. Georgiou, “On the recursive sequence ${x}_{n+1}=\alpha +{x}_{n-1}/{x}_{n}$,”
*Journal of Mathematical Analysis and Applications*, vol. 233, no. 2, pp. 790–798, 1999. View at Publisher · View at Google Scholar · View at MathSciNet - K. S. Berenhaut and S. Stević, “The behaviour of the positive solutions of the difference equation ${x}_{n}=A+{({x}_{n-2}/{x}_{n-1})}^{p}$,”
*Journal of Difference Equations and Applications*, vol. 12, no. 9, pp. 909–918, 2006. View at Publisher · View at Google Scholar · View at MathSciNet - S. Stević, “On the recursive sequence ${x}_{n+1}=\alpha +{x}_{n-1}^{p}/{x}_{n}^{p}$,”
*Journal of Applied Mathematics & Computing*, vol. 18, no. 1-2, pp. 229–234, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - H. M. El-Owaidy, A. M. Ahmed, and M. S. Mousa, “On asymptotic behaviour of the difference equation ${x}_{n+1}=\alpha +{x}_{n-1}^{p}/{x}_{n}^{p}$,”
*Journal of Applied Mathematics & Computing*, vol. 12, no. 1-2, pp. 31–37, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. DeVault, C. Kent, and W. Kosmala, “On the recursive sequence ${x}_{n+1}=p+{x}_{n-k}/{x}_{n}$,”
*Journal of Difference Equations and Applications*, vol. 9, no. 8, pp. 721–730, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - K. S. Berenhaut and S. Stević, “A note on positive non-oscillatory solutions of the difference equation ${x}_{n+1}=\alpha +{x}_{n-k}^{p}/{x}_{n}^{p}$,”
*Journal of Difference Equations and Applications*, vol. 12, no. 5, pp. 495–499, 2006. View at Publisher · View at Google Scholar · View at MathSciNet - K. S. Berenhaut, J. D. Foley, and S. Stević, “The global attractivity of the rational difference equation ${y}_{n}=A+{({y}_{n-m}/{y}_{n-k})}^{p}$,”
*Proceedings of the American Mathematical Society*, vol. 136, no. 1, pp. 103–110, 2008. View at Publisher · View at Google Scholar · View at MathSciNet - R. M. Abu-Saris and R. DeVault, “Global stability of ${y}_{n+1}=A+{y}_{n}/{y}_{n-k}$,”
*Applied Mathematics Letters*, vol. 16, no. 2, pp. 173–178, 2003. View at Google Scholar · View at MathSciNet - R. DeVault, G. Ladas, and S. W. Schultz, “On the recursive sequence ${x}_{n+1}=A/{x}_{n}+1/{x}_{n-1}$,”
*Proceedings of the American Mathematical Society*, vol. 126, no. 11, pp. 3257–3261, 1998. View at Publisher · View at Google Scholar · View at MathSciNet - R. DeVault, W. Kosmala, G. Ladas, and S. W. Schultz, “Global behavior of ${y}_{n+1}=(p+{y}_{n-k})/(q{y}_{n}+{y}_{n-k})$,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 47, no. 7, pp. 4743–4751, 2001. View at Google Scholar · View at MathSciNet - V. L. Kocić and G. Ladas,
*Global Behavior of Nonlinear Difference Equations of Higher Order with Applications*, vol. 256 of*Mathematics and Its Applications*, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993. View at MathSciNet - M. Saleh and M. Aloqeili, “On the rational difference equation ${y}_{n+1}=A+{y}_{n}/{y}_{n-k}$,”
*Applied Mathematics and Computation*, vol. 177, no. 1, pp. 189–193, 2006. View at Publisher · View at Google Scholar · View at MathSciNet - S. Stević, “On monotone solutions of some classes of difference equations,”
*Discrete Dynamics in Nature and Society*, vol. 2006, Article ID 53890, 9 pages, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. Stević, “On the recursive sequence ${x}_{n+1}=A+{x}_{n}^{p}/{x}_{n-1}^{p}$,”
*Discrete Dynamics in Nature and Society*, vol. 2007, Article ID 34517, 9 pages, 2007. View at Publisher · View at Google Scholar - S. Stević, “On the recursive sequence ${x}_{n+1}=A+{x}_{n}^{p}/{x}_{n-1}^{r}$,”
*Discrete Dynamics in Nature and Society*, vol. 2007, Article ID 40963, 9 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet - F. Sun, “On the asymptotic behavior of a difference equation with maximum,”
*Discrete Dynamics in Nature and Society*, vol. 2008, Article ID 243291, 6 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - T. Sun and H. Xi, “Global behavior of the nonlinear difference equation ${x}_{n+1}=f({x}_{n-s},{x}_{n-t})$,”
*Journal of Mathematical Analysis and Applications*, vol. 311, no. 2, pp. 760–765, 2005. View at Publisher · View at Google Scholar · View at MathSciNet - X. Yang, Y. Yang, and J. Luo, “On the difference equation ${x}_{n}=(p+{x}_{n-s})/(q{x}_{n-t}+{x}_{n-s})$,”
*Applied Mathematics and Computation*, vol. 189, no. 1, pp. 918–926, 2007. View at Publisher · View at Google Scholar · View at MathSciNet - Y. Yang and X. Yang, “On the difference equation ${x}_{n}=(p{x}_{n-s}+{x}_{n-t})/(q{x}_{n-s}+{x}_{n-t})$,”
*Applied Mathematics and Computation*, vol. 203, no. 2, pp. 903–907, 2008. View at Publisher · View at Google Scholar · View at MathSciNet