On the global asymptotic stability for a rational recursive sequence

Document Type: Regular Paper

Authors

1 Mathematics Department, Faculty of Science and Arts, Jazan University, Farasan, Jazan, Kingdom of Saudi Arabia

2 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

Abstract

The main objective of this paper is to study the boundedness character, the periodicity character, the convergence
and the global stability of the positive solutions of the nonlinear rational difference equation
/ , n 0,1,2,....
0 0
1  




 




  



 
k
i
i n i
k
i
n i n i x  x B  x
where the coefficients i i B , ,  together with the initial conditions ,.... , , 1 0 x x x k  are arbitrary
positive real numbers, while k is a positive integer number.

Keywords