Vector variational-type inequalities for set-valued mappings
This article deals with the generalized vector variational-type inequality problem of finding \(x_0\in K\) such that for all \(y\in K\) there exists \(s_0\in T(x_0)\) for which \[ \langle s_0, \theta(y, x_0)\rangle+ \eta(x_0, y)\not\in- \text{int }C(x_0), \] where \(K\) is a nonempty convex subset of a Hausdorff topological vector space \(X\), \(Y\) a topological vector space, \(T: K\to 2^{L(X, Y)}\), \(\theta: K\to X\), \(\eta: K\times K\to Y\) (\(L(X, Y)\) is the space of all continuous linear operators between \(X\) and \(Y\)), \(\{C(x): x\in K\}\) a family of closed convex cones in \(Y\). The main results are two theorems on solvability of the problem under considerations.
generalized vector variational-type inequality problem
scientific article; zbMATH DE number 1540356
scientific article