**MSC:**- 65J15 Equations with nonlinear operators (do not use 65Hxx)

convex and closed subset (solution set of a convex problem). Besides

let $Q\supseteq M$ be a further convex and closed subset (feasible

domain, constraints). We consider iterative methods

\[x_{k+1} \in g_k(x_k), x_0 \in Q \]

with point-to-set mappings $g_k:Q \rightarrow {\Bbb P} (Q)$, wich are

Fejer-monotone relative to $M$ (or $M$-Fejer-monotone). We present

conditions ensuring strong convergence of $(x_k)$ to a fixed element

$x^*$ in $M$. Finally we give applications of the results to various

types of convex.