A generalization of Naundorf's fixpoint theorem

Given is an ordered set in which every chain has an upper bound and every pair of elements has a greatest lower bound. Let Z be its set of maximal elements and let F be a function from Z to Z. A condition is presented that implies that F has a unique fixpoint. This is a generalization of a theorem of Naundorf. In Naundorf's theorem, the condition is related to causality for behaviour that develops in time.