The Dunkl-Williams constant related to Singer orthogonality and isosceles orthogonality in Banach spaces

Abstract

In this paper, we shall consider two new constants DW_S(X) and DW_I(X), which are the Dunkl-Williams constant related to Singer orthogonality and isosceles orthogonality, respectively. Some estimates for these two constants are established. We discuss the relationships between DW_S(X) and some geometric properties of Banach spaces, including uniform non-squareness, uniform convexity. Furthermore, an equivalent form of DW_S(X) in the symmetric Minkowski planes is given and used to compute the value of DW_S((R2, ∥ · ∥p)), 1 < p < ∞, and we also give a characterization of the Radon plane with affine regular hexagonal unit sphere in terms of DW_S(X).