NONLINEAR MEAN ERGODIC THEOREMS

Abstract

Let $C$ be a nonempty subset (not necessarily closed and convex) of a Hilbert space, and $T: C \rightarrow C$ be a nonlinear mapping (not necessarily asymptotically nonexpansive). In this paper, we study the convergence of $(1/n)\sum^{n-1}_{i=0} T^i x(x\in C)$ as $n \rightarrow \infty $.