  This paper is focused on some properties of paramonotone operators on Banach
spaces and their application to certain feasibility problems for convex sets in
a Hilbert space and convex systems in the Euclidean space. In particular, it
shows that operators that are simultaneously paramonotone and bimonotone are
constant on their domains, and this fact is applied to tackle two particular
situations. The first one, closely related to simultaneous projections, deals
with a finite amount of convex sets with an empty intersection and tackles the
problem of finding the smallest perturbations (in the sense of translations) of
these sets to reach a nonempty intersection. The second is focused on the
distance to feasibility; specifically, given an inconsistent convex inequality
system, our goal is to compute/estimate the smallest right-hand side
perturbations that reach feasibility. We advance that this work derives lower
and upper estimates of such a distance, which become the exact value when
confined to linear systems.
