Some New James Type Geometric Constants in Banach Spaces

Abstract

We will introduce four new geometric constants closely related to the James constant J(X), which have symmetric structure, along with a discussion on the relationships among them and some other well-known geometric constants via several inequalities, together with the calculation of several values on some specific spaces. In addition, we will characterize geometric properties of J1(X), such as uniform non-squareness and uniformly normal structure.