An intersection theorem for set-valued mappings (Q375435)

The paper presents an interesting theorem on a fixed point of a multivalued mapping which is simultaneously a common point for the family of values of another multivalued mapping. The proof is based on the Himmelberg theorem (which is a generalization of Kakutani-Fan-Glicksberg fixed point theorem) and on the partition of unity on a compact set. Applications to common fixed point theorems, saddle point theorems, as well as the solutions of equilibrium and complementarity problems are given.