We show nonlinear ergodic theorems for commutative semigroups of lipschitzian mappings. We first prove the existence of a retraction P of C onto F(G) such that PT_(t) = T_(t)P = P for every t ∈ G. Secondly, we show that if E has a Frechet differenti...
We show nonlinear ergodic theorems for commutative semigroups of lipschitzian mappings. We first prove the existence of a retraction P of C onto F(G) such that PT_(t) = T_(t)P = P for every t ∈ G. Secondly, we show that if E has a Frechet differentiable norm, then such a retraction P is unique.