Loose saddle points of set-valued maps in topological vector spaces

We give a new existence theorem for loose saddle point of set-valued map ha ving values in a partially ordered topological vector space which is based on continuity and quasiconvexity-quasiconcavity of its scalarized maps. Mor eover, we prove a nea saddle point theorem for vector-valued functions in l ocally convex topological vector spaces under weak condition that is the se micontinuity of two function scalarization. (C) 1999 Elsevier Science Ltd. All rights reserved.