  The present paper contains some investigations about a uniform variant of the
notion of metric hemiregularity, the latter being a less explored property
obtained by weakening metric regularity. The introduction of such a
quantitative stability property for set-valued mappings is motivated by
applications to the penalization of constrained optimization problems, through
the notion of problem calmness. As a main result, an implicit multifunction
theorem for parameterized inclusion problems is established, which measures the
uniform hemiregularity of the related solution mapping in terms of problem
data. A consequence on the exactness of penalty functions is discussed.
