The global attractivity of difference equations of nonincreasing nonlinearities with applications. (Q1416437)

The author studies the global attractivity of the unique positive equilibrium of the equation \(x_{n+1}=g(x_{n-k_1},x_{n-k_2},\dots,x_{n-k_m}),\;n=0,1,2,\dots\), where \(g\) is a nonincreasing continuous function in each of its arguments and the \(k\) are positive integers. The obtained results extend previous ones by \textit{M. Arciero, G. Ladas}, and \textit{S. W. Schultz} in [Georgian Math. J. 1, 229--233 (1994; Zbl 0808.39003)]. An application is made for the discrete Clark model \(x_{n+1}=\alpha x_n+f(x_{n-k})\) and the rational recursive sequence \(x_{n+1}=(a+bx_n)/(A+x_{n-1})\).