  In this paper, we consider some equilibrium problems (or saddle point
problems), in which the domains of the considered mappings are limited at some
regions. These restricted regions are defined by some mappings which are called
the constrained mappings in the given problems. For this reason, we introduce
the concepts of constrained ordered equilibrium problems, that are useful
extensions of ordered equilibrium problems and ordinary equilibrium problems.
Then, by using some fixed point theorems on posets, we prove several theorems
for existence of solutions to some constrained ordered equilibrium problems. In
particular, we investigate the solvability of some constrained ordered
equilibrium problems in some partially ordered Banach spaces.
