Summary: A result of F. E. Browder states that if \(T\) is a monotone and hemicontinuous map of a closed convex set \(K\) in a reflexive real Banach space \(X\), with \(0\in K\), into the dual space \(X^*\) (\(T\) is coercive on \(K\) if \(K\) is not bounded) then there exists \(x_ 0\in K\) such that \((Tx_ 0,y-x_ 0)\geq 0\) for all \(y\in K\). In this note a certain generalization of this result is presented.