Fixed point theorems for multifunctions having KKM property on almost convex sets

In this paper, for two nonempty subsets X and Y of a linear space E, we define the class KKM(X,Y ) and investigate the fixed point problem for T ∈ KKM(X,X) with X an almost convex subset of a locally convex space. Our fixed point theorem contains Lassonde fixed point theorem for Kakutani factorizable multifunctions as special case.  2005 Elsevier Inc. All rights reserved.