Abstract
IIn this paper, we deal with a class of nonexpansive mappings with the property $D(\overline{co} F_{\frac 1n} (T),F(T))\to 0$, as $n\to \infty$, where $D$ is the Hausdorff metric. We show that nonexpansive mappings with compact domains enjoy this property and give some examples of this kind of mappings with noncompact domains in $l^\infty$. Then we prove a nonlinear ergodic theorem, and a convergence theorem of mann's type for this kind of mappings.
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