Characterization of metric regularity for σσ-subsmooth multifunctions

In terms of the coderivative, we provide characterizations of metric subregularity for σσ-subsmooth multifunctions and extend some existing results on metric subregularity. We also establish Robinson–Ursescu type theorems for σσ-subsmooth multifunctions and approximately convex multifunctions. As applications, we study error bounds for nonconvex inequalities and Lipschitz property for multifunctions.