Asymptotic behavior of solutions of difference equations in Banach spaces
Asymptotic behavior of solutions of difference equations in Banach spaces
In this paper we consider the first order difference equation \[ \Delta x_n = \sum _{i=0}^\infty a_n^i f(x_{n+i}), \] and give necessary and sufficient conditions so that there exist solutions which are asymptotically constant. These results generalize those given earlier by Popenda and Schmeidel. As an application we give necessary …