On the global asymptotic stability for a rational recursive sequence

Abstract

The main objective of this paper is to study the boundedness character, the periodicity character, the convergenceand the global stability of the positive solutions of the nonlinear rational difference equation/ , n 0,1,2,....0 01      kii n ikin i n i x  x B  xwhere the coefficients i i B , ,  together with the initial conditions ,.... , , 1 0 x x x k  are arbitrarypositive real numbers, while k is a positive integer number.