We show some sufficient conditions on a Banach space X concerning the generalized James constant, the generalized Jordan-von Neumann constant, the generalized Zbagănu constant, the coefficient ε ˜ 0 ( X ) , the weakly convergent sequence coefficient WCS ( X ), and the coefficient of weak orthogonality, which imply the existence of fixed points for multivalued nonexpansive mappings. These fixed point theorems improve some previous results in the recent papers.