Global attractivity for a class of higher order nonlinear difference equations. (Q1427886)

The authors study the global attractivity of positive solutions of a class of difference equations of the form \(x_{n+1}= (a-bx_n)/(A-\sum_{i=0}^k b_ix_{n-i})\) for \(n=0,1,\cdots\), where the constants \(A,b,b_k\) are positive and \(a, b_0,\cdots ,b_{k-1}\) are nonnegative. They show that one positive equilibrium \(\bar x\) of this equation is a global attractor with a basin that can be estimated in several cases.