[efr-ECP8]

Let f: A \to A be a sup-preserving endomorphism of a domain. Then we can find a fixpoint by defining T(x) = x \vee f(x) and iterating this starting at \bot ---this is "Tarski iteration"

Now if f is instead a map between convex sets in a vector space, we can do Tx = \frac {1}{2}(x + f(x)), and iterate this. Under some continuity assumptions this converges weakly to a fixpoint---this is Krasonelskii-Mann iteration.

Now, recall that defining \alpha x + (1-\alpha )y = x \vee y for \alpha \in (0,1) gives a convex structure to any semilattice. This provides a unification of these two ideas.