Equilibrium problems when the equilibrium condition is missing

Abstract Given a nonempty convex subset X of topological vector space and real bifunction f defined on $$X \times X$$ X × , the associated equilibrium problem consists in finding point $$x_0 \in x 0 ∈ such that $$f(x_0, y) \ge 0$$ f ( , y ) ≥ for all $$y . A standard condition problems is values to be nonnegative diagonal In this paper, we deal with which missing. For purpose, will need consider, besides function another one $$g: \rightarrow \mathbb {R}$$ g : → R two bifunctions being linked by certain compatibility condition. Applications variational inequality problems, quasiequilibrium are given.