Variational inequality problem in Hausdorff topological vector spaces
The authors considered the generalized variational type inequality problem: Find \(\overline x\in K\), such that \[ \langle T(\overline x),g(y,\overline x)\rangle\geq 0\quad\text{for all }\overline x\in K, \] where \(K\) is a nonempty convex subset of a Hausdorff topological space \(X\) with dual space \(X^*\), \(T:K\to X^*\), \(G:K\times K\to X\). They use a KKM theorem of Fan to establish existence theorems of the above inequality. If \(g(y,x)= y-f(x)\), where \(f:K\to K\) is a continuous function, then the problem reduces to the case considered by Isac.
scientific article; zbMATH DE number 1013750