ON ESSENTIAL COMPONENTS OF CRITICAL POINTS FOR SET-VALUED MAPPINGS

Abstract

We introduce the notion of an essential component to the set of critical points for set-valued mappings, then we prove that there exists at least one essential component to the set of critical points for set-valued mappings satisfying some conditions. Moreover, we deduce that there exists at least one essential component to the set of fixed points for non-self set-valued mappings.