Global asymptotic stability of inhomogeneous iterates (Q1607826)

Summary: Let \((M,d)\) be a finite-dimensional complete metric space, and \(\{T_{n}\}\) a sequence of uniformly convergent operators on \(M\). We study the non-autonomous discrete dynamical system \(x_{n+1} = T_{n}x_{n}\) and the globally asymptotic stability of the inhomogeneous iterates of \(\{T_{n}\}\). Then we apply the results to investigate the stability of equilibrium of \(T\) when it satisfies certain type of sublinear conditions with respect to the partial order defined by a closed convex cone. The examples of application to nonlinear difference equations are also given.