Existence theorems via duality for equilibrium problems with trifunctions

Abstract

We present an existence result for an equilibrium problem formulated with trifunctions, which is motivated by variational inequalities governed by quasimonotone operators. To prove the existence result, we define the dual problem, and some monotonicity notions for trifunctions. From the main result follow, among others, the Browder–Minty theorem for variational inequalities and Ky Fan’s Minimax theorem. Some applications for mixed equilibrium problems and variational inequalities are given.

Keywords:

• Equilibrium problems
• variational inequalities
• saddle points
• monotonicity
• duality

Notes

No potential conflict of interest was reported by the authors.