Computing Kakutani Fixed Points

Let C be a compact convex subset of $R^m $, let $C^ * $ be the set of compact convex subsets of C, and let $f:C \to C^ * $ be a closed (i.e., upper semicontinuous) point-to-set map. An algorithm is specified which generates a sequence of points in C such that every cluster point x is a fixed point of f (i.e., $x \in f( x ) $).