A generalization of the $({\alpha},{\beta},{\gamma})$ von Neumann-Jordan type constant in Banach spaces

In this paper,motivated by the pioneering work of Moslehian and Rassias, we introduce a novel generalized von Neumann-Jordan type constant in Banach spaces, a constant that notably encompasses a range of classical geometric constants.

First, we establish the bounds of this constant within Banach spaces.

Next, we derive its relationships with other geometric constants.

Furthermore, we characterize the uniformly non-square property and provide a sufficient condition for the uniform normal structure by leveraging this newly proposed constant.