Some geometric conditions which imply the fixed point property for multivalued nonexpansive mappings

We show some geometric conditions on a Banach space X concerning the modulus of smoothness, the coefficient of weak orthogonality, the coefficient R(a,X), the James constant and the Jordan–von Neumann constant, which imply the existence of fixed points for multivalued nonexpansive mappings. These fixed point theorems improve some previous results and give affirmative answers to some open questions.