Characterization of Calmness for Banach space mappings

Abstract

We characterize calmness of multifunctions explicitly by calmness of level sets to globally Lipschitz functions, by convergence of specific solution methods for the related inclusions as well as by solvability of crucial linear systems. As a main tool, a so-called relative slack function will be applied. In this way, also equivalence between calmness and metric regularity of specific subsystems will be derived.