文摘
We introduce a new geometric constant \(C_{NJ}^{(p)}(X)\) for a Banach space X, called a generalized von Neumann-Jordan constant. Next, it is shown that \(1\leq C_{NJ}^{(p)}(X)\leq2\) for any Banach space X and that the right hand side inequality is sharp if and only if X is uniformly non-square. Moreover, a relationship between the James constant \(J(X)\) and \(C_{NJ}^{(p)}(X)\) is presented. Finally, the generalized von Neumann-Jordan constant of the Lebesgue space \(L_{r}([0,1])\) is calculated and a relationship between \(C_{NJ}^{(p)}(X)\) and the fixed point property is found.