  For an ascending correspondence $F:X\to 2^X$ with chain-complete values on a
complete lattice $X$, we prove that the set of fixed points is a complete
lattice. This strengthens Zhou's fixed point theorem. For chain-complete posets
that are not necessarily lattices, we generalize the Abian-Brown and the
Markowsky fixed point theorems from single-valued maps to multivalued
correspondences. We provide an application in game theory.
