Path stability and nonlinear weak ergodic theorems

Abstract

Let{fn}\{f_{n} \}be a sequence of nonlinear operators. We discuss the asymptotic properties of their inhomogeneous iteratesfn∘fn−1∘⋯∘f1f_{n} \circ f_{n-1} \circ \cdots \circ f_{1}\,in metric spaces, then apply the results to the ordered Banach spaces through projective metrics. Theorems on path stability and nonlinear weak ergodicity are obtained in this paper.