Springer Iranian Journal of Science and Technology (Sciences) 1028-6276 35 4 2011 12 06 On the global asymptotic stability for a rational recursive sequence 333 339 2159 10.22099/ijsts.2011.2159 EN E. M. E. Zayed Mathematics Department, Faculty of Science and Arts, Jazan University, Farasan, Jazan, Kingdom of Saudi Arabia A. El-Moneam Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt Present address: Mathematics Department, Faculty of Science and Arts, Jazan University, Farasan, Jazan, Kingdom of Saudi Arabia Journal Article 2011 01 04 The main objective of this paper is to study the boundedness character, the periodicity character, the convergence<br />and the global stability of the positive solutions of the nonlinear rational difference equation<br />/ , n 0,1,2,....<br />0 0<br />1  <br /><br /><br /><br /><br /> <br /><br /><br /><br /><br />  <br /><br /><br /><br /> <br />k<br />i<br />i n i<br />k<br />i<br />n i n i x  x B  x<br />where the coefficients i i B , ,  together with the initial conditions ,.... , , 1 0 x x x k  are arbitrary<br />positive real numbers, while k is a positive integer number. https://ijsts.shirazu.ac.ir/article_2159_22ac2ec666f4144d2791a7a9a9bcce24.pdf