Fixed point properties related to multivalued mappings (Q978967)

The main result of this paper is the following: Let \(X\) be a paracompact convex subset of a locally convex linear topological space. Then the following statements are equivalent: (1) \(X\) has the fixed point property; (2) \(X\) has the Browder fixed point property; (3) \(X\) has the open graph fixed point property; (4) \(X\) has the weak Kakutani fixed point property; (5) \(X\) has the Kakutani fixed point property.