On a new geometric constant related to the von Neumann–Jordan constant

The von Neumann–Jordan constant CNJ(X) is computed for X being ℓ2−ℓ1 and ℓ∞−ℓ1 space by introducing a new geometric constant γX(t). These partly give an answer to an open question posed by Kato et al. Some basic properties of this new coefficient are investigated. Moreover, we obtain a new class of Banach spaces with uniform normal structure.