Existence theorems via duality for equilibrium problems with trifunctions. (4th May 2018)

• Record Type: Journal Article
• Authors: Inoan, D.; Kolumbán, J.
• Is Part Of: Optimization. Volume 67:Number 5(2018)
• Page Start: 537
• Page End: 547
• Publication Date: 2018-05-04
• Subjects: Equilibrium problems -- variational inequalities -- saddle points -- monotonicity -- duality; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1446956
• Languages: English
• ISSNs: 0233-1934

Abstract

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.