This article deals with iterates
where , is a sequence from , a sequence from , a maximal monotone operator in a real Hilbert space. The basic results are
(a) a theorem about strong convergence of iterates (1) to , where is the metric projection onto ;
(b) a theorem about weak convergence of iterates (2) to , where is the metric projection onto .
In the end of the article the special case when is considered, where is a proper lower-semicontinuous convex function. The corresponding results is interpreted as theorems of finding a minimizer of .