Another generalized angle related to norm derivatives in Banach spaces

Motivated by recent work on generalized angles in Banach spaces, we introduce a new angle Aρ (x,y) based on norm derivatives for two nonzero vectors x and y. We first study its elementary properties and then use it to characterize strict convexity in Banach spaces. Furthermore, we define two new geometric constants D_ρ^B (X) and D_g^B (X), induced from norm derivatives. We explore the relationship between D_ρ^B (X) and existing geometric constants, as well as properties like non-squareness and uniform convexity. A characterization of the Radon plane with an affine-regular hexagonal unit sphere is given in termρs of D_ρ^B (X). Finally, we establish some estimates for D_g^B (X) and connect it to non-squareness.