On nonlinear variational inequalities
E Tarafdar · Proceedings of the American Mathematical Society · 1977
In this note we have given a direct proof of the result which states that if K is a compact convex subset of a linear Hausdorff topological space E over the reals and T is a monotone and hemicontinuous (nonlinear) mapping of K into E ∗ {E^ \ast } , then there is a u 0 ∈ K {u_0} \in K such that ( T ( u 0 ) , v − u 0 ) ⩾ 0 (T({u_0}),v - {u_0}) \geqslant 0 for all v ∈ K v \in K .