Sufficient conditions to guarantee unique fixpoint (not unique least/greatest fixpoint) for monotone functions on complete lattice
Constant functions have unique fixed points. Another criterion that may be applicable is to compare approximations, $\mu_i = \bigcup_{k&lt;i}f^k(\bot)$ and $\nu_i = \bigcap_{k&lt;i}f^k(\top)$, of the least and the greatest fixed points. Trivially, as soon as $\mu_i = \nu_i$ for some $i$, it has been settled that $f$ has a unique fixed point. The problem with this characterization is that, depending on the lattice and $f$, it is incomplete unless you are prepared to explore transfinite approximations.