Normal structure and generalized von Neumann-Jordan type constant

We introduce the generalized von Neumann-Jordan type constant of a Banach space and give some geometric properties concerning this new coefficient. Moreover, we establish several sufficient conditions for normal structure of a Banach space in terms of the generalized von Neumann-Jordan type constant, the generalized James constant, the coefficient of weak orthogonality and the generalized García-Falset coefficient. Our main results in this paper significantly improve and generalize many known results in the literature.