Characterizations of error bounds for convex multifunctions on Banach spaces

In terms of various derivatives such as contingent derivative and Dini-derivative, we give a series of characterizations of error bounds for convex multifunctions defined on Banach spaces, extending Lewis and Pang's result on a characterization of the existence of global error bounds for approximate solutions of convex inequalities in Euclidean spaces. Applications are given not only to improve some known results but also to provide new results on the existence of error bounds for not necessarily lower semicontinuous convex functions.