Abstract
In this paper, we shall consider two new constants DWS(X) and DWI(X), which are the Dunkl-Williams constant related to the Singer orthogonality and theisosceles orthogonality, respectively. We discuss the relationships between DWS(X) and some geometric properties of Banach spaces, including uniform non-squareness, uniform convexity. Furthermore, an equivalent form of DWS(X) in the symmetric Minkowski planes is given and used to compute the value of DWS((R2, ???p)), 1 < p < ?, and we also give a characterization of the Radon plane with affine regular hexagonal unit sphere in terms of DWS(X). Finally, we establish some estimates for DWI(X) and show that DWI(X) does not necessarily coincide with DWS(X).
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