For given nonempty sets \(A\), \(B\) and the function \(\varphi: A\times B\to\mathbb{R}\), consider the problem of finding \(u\in A\) such that \[ \varphi(u,v)\geq 0\quad\text{for every }v\in B.\tag \] It is shown that the problem (1) generalizes the minimum problem, saddle point, variational inequality, and the equilibrium problems. The authors have proved that main results can be obtained as simple applications of the well-known separation theorems of convex sets in finite-dimensional spaces. This paper contains some new interesting and novel results.