A variational principle for vector equilibrium problems
The author describes a variational principle for vector equilibrium problems of finding \(x\in K\) such that \[ f(x,y)\not\in -\text{int }P \] for all \(y\in K\), where \(\text{ int}P\) denotes the topological interior of the cone \(P\), \(X\) is a real topological vector space, \(K\) is a nonempty closed convex subset of \(X\), \((Y,P)\) is a real ordered topological vector space, and \(f:X\times X\to Y\) is a mapping with \(f(x,x)=0\) for all \(x\in X\). Under some conditions, the author analyses the solutions for vector equilibrium problems and obtains some new results.
scientific article; zbMATH DE number 1740620