On scalar equilibrium problem in generalized convex spaces (Q874956)

The author proves the existence of a solution to the scalar equilibrium problem: find \(x_0\in K\) such that \(f(x_0,y)\geq 0\) for all \(y\in K\), where \(K\) is a given subset of a generalized convex space and \(f:K\times K\to \mathbb{R}\) a given function, \(f(x,x)\geq 0\) for all \(x\in K\). Applications to best approximations and to simultaneous approximations are presented.