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 having values in a partially ordered topological vector space which is based on continuity and quasiconvexity-quasiconcavity of its scalarized maps. Moreover, we prove a nea saddle point theorem for vector-valued functions in locally convex topological vector spaces under weak condition that is the semicontinuity of two function scalarization. (C) 1999 Elsevier Science Ltd. All rights reserved.