Normal Structure and Generalized Von Neumann-Jordan Type Constant

Abstract

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 the 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 of Sims and the generalized Garcia-Falset coefficient. Our main results in this paper significantly improve and generalize many known results in the literatures.