Given a complete partial order $(D,\, {\leq})$ and a Scott-continuous function $F\colon D \rightarrow D$ and some fixed point $X = F(X)$. Are there any criteria that ensure that $X = \mathsf{lfp} F$ where $\mathsf{lfp} F$ is the least fixed point of $F$?Furthermore, are there any criteria that ensure that $Y \leq \mathsf{lfp} F$ for an arbitrary point $Y$?
Criteria for being below the least fixed point
domain theory