The Dunkl–Williams Constant Related to Birkhoff Orthogonality in Banach Spaces

In this paper, we shall consider a new constant DW pB (l∞ − l1). which is the Dunkl-Williams constant related to Birkhoff orthogonality, and a constant [[EQUATION]]that is a generalization of DW pB (l∞ − l1). Interestingly, the upper bounds of DW pB (l∞ − l1) and the Dunkl-Williams constant are different. The connections between these two constants and other well-known constants are exhibited. Some characterizations of Hilbert space and uniformly non-square Banach space in terms of these two constants are established. Furthermore, we also give a characterization of the Radon plane with affine regular hexagonal unit sphere and calculate the value of DW pB (l∞ − l1).