Let C be a convex subset of a nuclear locally convex space that is also an -F-space. Suppose T:C -> C is nonexpansive and {v n } is given by the Mann iteration process. It is shown that if {v n } is bounded, T has a fixed point. Also, a sequence {y n } can be constructed such that y n -+y weakly where Ty = y. If C is a linear subspace and T is linear, then lim y n = y