Existence of zero points for pseudomonotone operators in Banach spaces (Q1016071)

Based on the KKM principle by Ky Fan and on a minimax theorem of Kneser, the authors prove an existence result of zero points for pseudomonotone set-valued operators \(T:X\to 2^{E^*}\), where \(X\) is a nonempty closed convex subset of a Banach space \(E\). A necessary and sufficient condition for the existence of zero points is given for the case \(X=E\) and \(E\) be a reflexive Banach space.