Three Kinds of Denting Points and Their Further Applications in Banach Spaces

In this paper, we study three kinds of dentabilities and present their important applications in the geometric theory of Banach spaces. First, the relations between weak-denting points and extreme points are established. Moreover, we characterize strong convex spaces and weakly locally uniformly smooth spaces by using weakly locally uniform dentability. Finally, we provide some important applications of strong∗ dentability in Fréchet-smooth Banach spaces while investigating the density of strong∗ points in dual Banach spaces.