In this paper, we shall consider a new constant \(DW_B(X)\) which is the Dunkl–Williams constant related to Birkhoff orthogonality, and a constant \(DW^p_B(X)\) that is a generalization of \(DW_B(X)\). Interestingly, the upper bounds of \(DW_B(X)\) 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 an affine regular hexagonal unit sphere and calculate the value of \(DW^p_B(l_\infty -l_1)\).

在本文中，我们将考虑一个新常数\(DW_B(X)\)，它是与 Birkhoff 正交性相关的 Dunkl-Williams 常数，以及一个常数\(DW^p_B(X)\)，它是\( DW_B(X)\)。有趣的是， \(DW_B(X)\)和 Dunkl-Williams 常数的上限是不同的。展示了这两个常数和其他众所周知的常数之间的联系。建立了希尔伯特空间和一致非方巴纳赫空间关于这两个常数的一些表征。此外，我们还给出了具有仿射正六边形单位球面的氡平面的表征，并计算了\(DW^p_B(l_\infty -l_1)\)的值。