On a generalized geometric constant and sufficient conditions for normal structure in Banach spaces

In this paper, we introduce a new geometric constant CNJ(p)(a,X) of a Banach space X, which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant. Subsequently, we present several sufficient conditions for normal structure of a Banach space in terms of this new constant, the generalized James constant, the generalized García-Falset coefficient and the coefficient of weak orthogonality of Sims. Our main results of the paper generalize some known results in the recent literature.