Discrete Dynamics in Nature and Society

Volume 2007, Article ID 39404, 7 pages

http://dx.doi.org/10.1155/2007/39404

Research Article

## On the Recursive Sequence x n = 1 + ∑ i = 1 k α i x n − p i / ∑ j = 1 m β j x n − q j

Mathematical Institute of the Serbian Academy of Sciences and Arts
, Knez Mihailova 35/I, Belgrade 11001, Serbia

Received 28 September 2006; Revised 3 December 2006; Accepted 11 December 2006

Copyright © 2007 Stevo Stević. 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

- K. Berenhaut, J. Foley, and S. Stević, “The global attractivity of the rational difference equation ${y}_{n}=1+{{y}_{n-k}/y}_{n-m}$,”
*Proceedings of the American Mathematical Society*, vol. 135, no. 4, pp. 1133–1140, 2007. View at Publisher · View at Google Scholar - R. M. Abu-Saris and K. Y. Al-Hami, “A global convergence criterion for higher order nonlinear difference equations with applications,”
*Journal of Difference Equations and Applications*, vol. 12, no. 9, pp. 901–907, 2006. View at Publisher · View at Google Scholar - K. S. Berenhaut, J. D. Foley, and S. Stević, “Quantitative bounds for the recursive sequence
${y}_{n+1}=A+{{y}_{n}/y}_{n-k}$,”
*Applied Mathematics Letters*, vol. 19, no. 9, pp. 983–989, 2006. View at Publisher · View at Google Scholar · View at MathSciNet - L. Berg, “On the asymptotics of nonlinear difference equations,”
*Zeitschrift für Analysis und ihre Anwendungen*, vol. 21, no. 4, pp. 1061–1074, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - L. Berg and L. von Wolfersdorf, “On a class of generalized autoconvolution equations of the third kind,”
*Zeitschrift für Analysis und ihre Anwendungen*, vol. 24, no. 2, pp. 217–250, 2005. View at Google Scholar · 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 - E. A. Grove and G. Ladas,
*Periodicities in Nonlinear Difference Equations*, vol. 4 of*Advances in Discrete Mathematics and Applications*, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2005. View at Zentralblatt MATH · View at MathSciNet - G. Karakostas, “Convergence of a difference equation via the full limiting sequences method,”
*Differential Equations and Dynamical Systems*, vol. 1, no. 4, pp. 289–294, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - G. Karakostas, “Asymptotic 2-periodic difference equations with diagonally self-invertible responses,”
*Journal of Difference Equations and Applications*, vol. 6, no. 3, pp. 329–335, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - W. Kosmala and C. Teixeira, “More on the difference equation ${y}_{n+1}=\left(p+{y}_{n}\right)/\left(q{y}_{n}+{y}_{n-1}\right)$,”
*Applicable Analysis*, vol. 81, no. 1, pp. 143–151, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - I. Niven and H. S. Zuckerman,
*An Introduction to the Theory of Numbers*, John Wiley & Sons, New York, NY, USA, 2nd edition, 1966. View at Zentralblatt MATH · View at MathSciNet - S. Stević, “A note on periodic character of a difference equation,”
*Journal of Difference Equations and Applications*, vol. 10, no. 10, pp. 929–932, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. Stević, “On the recursive sequence
${x}_{n+1}=(\alpha +\beta {x}_{n-k})/f\left({x}_{n},\dots ,{x}_{n-k+1}\right)$,”
*Taiwanese Journal of Mathematics*, vol. 9, no. 4, pp. 583–593, 2005. View at Google Scholar · View at MathSciNet - T. Sun, H. Xi, and H. Wu, “On boundedness of the solutions of the difference equation ${x}_{n+1}={x}_{n-1}/\left(p+{x}_{n}\right)$,”
*Discrete Dynamics in Nature and Society*, vol. 2006, Article ID 20652, p. 7, 2006. View at Publisher · View at Google Scholar - S.-E. Takahasi, Y. Miura, and T. Miura, “On convergence of a recursive sequence
${x}_{n+1}=f\left({x}_{n},{x}_{n-1}\right)$,”
*Taiwanese Journal of Mathematics*, vol. 10, no. 3, pp. 631–638, 2006. View at Google Scholar · View at MathSciNet - X.-X. Yan, W.-T. Li, and Z. Zhao, “On the recursive sequence
${x}_{n+1}=\alpha -\left({x}_{n}/{x}_{n-1}\right)$,”
*Journal of Applied Mathematics & Computing*, vol. 17, no. 1-2, pp. 269–282, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet