Affiliation:
1. Department of Mathematics, Sun Yat-sen University, Guangzhou, P.R. China
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).
Publisher
National Library of Serbia
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