Discrete Dynamics in Nature and Society
Volume 2007, Article ID 91292, 7 pages
http://dx.doi.org/10.1155/2007/91292
Research Article

## A Global Convergence Result for a Higher Order Difference Equation

Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, Beograd 11000, Serbia

Received 9 February 2007; Revised 15 April 2007; Accepted 13 June 2007

Copyright © 2007 Bratislav D. Iričanin. 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.

1. J. Bibby, “Axiomatisations of the average and a further generalisation of monotonic sequences,” Glasgow Mathematical Journal, vol. 15, pp. 63–65, 1974.
2. D. Borwein, “Convergence criteria for bounded sequences,” Proceedings of the Edinburgh Mathematical Society (2), vol. 18, no. 1, pp. 99–103, 1972/73.
3. E. T. Copson, “On a generalisation of monotonic sequences,” Proceedings of the Edinburgh Mathematical Society (2), vol. 17, no. 2, pp. 159–164, 1970/71.
4. H. El-Metwally, E. A. Grove, and G. Ladas, “A global convergence result with applications to periodic solutions,” Journal of Mathematical Analysis and Applications, vol. 245, no. 1, pp. 161–170, 2000.
5. G. L. Karakostas and S. Stević, “Slowly varying solutions of the difference equation ${x}_{n+1}=f\left({x}_{n},\dots ,{x}_{n-k}\right)+g\left(n,{x}_{n},{x}_{n-1},\dots ,{x}_{n-k}\right)$,” Journal of Difference Equations and Applications, vol. 10, no. 3, pp. 249–255, 2004.
6. S. Stević, “A note on bounded sequences satisfying linear inequalities,” Indian Journal of Mathematics, vol. 43, no. 2, pp. 223–230, 2001.
7. S. Stević, “A generalization of the Copson's theorem concerning sequences which satisfy a linear inequality,” Indian Journal of Mathematics, vol. 43, no. 3, pp. 277–282, 2001.
8. S. Stević, “A global convergence result,” Indian Journal of Mathematics, vol. 44, no. 3, pp. 361–368, 2002.
9. S. Stević, “A global convergence results with applications to periodic solutions,” Indian Journal of Pure and Applied Mathematics, vol. 33, no. 1, pp. 45–53, 2002.
10. S. Stević, “Asymptotic behavior of a sequence defined by iteration with applications,” Colloquium Mathematicum, vol. 93, no. 2, pp. 267–276, 2002.
11. S. Stević, “Asymptotic behavior of a nonlinear difference equation,” Indian Journal of Pure and Applied Mathematics, vol. 34, no. 12, pp. 1681–1687, 2003.
12. K. S. Berenhaut and S. Stević, “The behaviour of the positive solutions of the difference equation ${x}_{n}=A+{\left({x}_{n-2}/{x}_{n-1}\right)}^{p}$,” Journal of Difference Equations and Applications, vol. 12, no. 9, pp. 909–918, 2006.
13. L. Berg, “Inclusion theorems for non-linear difference equations with applications,” Journal of Difference Equations and Applications, vol. 10, no. 4, pp. 399–408, 2004.
14. L. Berg, “Corrections to `inclusion theorems for non-linear difference equations with applications',” Journal of Difference Equations and Applications, vol. 11, no. 2, pp. 181–182, 2005.
15. 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.
16. S. Stević, “On the recursive sequence ${x}_{n}=1+{\sum }_{i=1}^{k}{\alpha }_{i}{x}_{n-{p}_{i}}/{\sum }_{j=1}^{m}{\beta }_{j}{x}_{n-{q}_{j}}$,” Discrete Dynamics in Nature and Society, vol. 2007, Article ID 39404, p. 7, 2007.
17. 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.
18. 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.