Variational inequalities and surjectivity for set-valued monotone mappings
The authors establish an existence theorem for a variational inequality of the type: Find \((y,w)\) in the graph of \(T\) such that \(\text{Re}\langle w,x-y\rangle\) is nonnegative for all \(x\) in \(X\). \(X\) is a convex set, and \(T\) is a monotone multivalued mapping. Appropriate compactness conditions are also assumed. The existence result is proved with the help of a standard KKM theorem. As an application, the authors provide a surjectivity criterion for the multivalued mapping \(T\).
scientific article; zbMATH DE number 1279192