Another generalized angle related to norm derivatives in Banach spaces

Abstract

Motivated by recent progress in the generalized angles in Banach spaces, we shall consider another angle Aρ(x, y), which is closely related to norm derivatives, between two nonzero vectors x and y in Banach spaces. We first discuss some basic properties of this angle Aρ(x, y). Moreover, we apply the angle to check whether or not a Banach space is strictly convex. Next, we introduce two new geometric constants DB ρ(X) and DB g(X), which are related to norm derivatives. We describe some relations between DB ρ(X) and some existing geometric constants as well as some geometric properties, such as non-squareness and uniform convexity. In addition, we also provide a characterization of the Radon plane with affneregular hexagonal unit sphere in terms of DB ρ(X). Finally, we derive some estimates for DBg(X) and the relation between the constant DB ρ(X) and non-squareness.