Error bounds for convex constrained systems in Banach spaces

In this paper, we first establish both primal (involving directional derivatives and tangent cones) and dual characterizations (involving subdifferential and normal cones) for the local (global) error bounds of constrained set-valued systems; as an application, we then derive both primal and dual characterizations for the local (global) error bounds of the constrained convex inequality systems in a general Banach space and also some sufficient conditions. The obtained results improve or generalize some known results.