Existence theorems via duality for equilibrium problems with trifunctions. (English) Zbl 1408.90289
This paper deals with generalized monotonicity and pesudomonotonicity for trifunctions, and presents sufficient conditions for the equivalence between the primal and the dual problems. The main results consist of the extension of some known existence theorems for equilibrium problems with bifunctions to the case of trifunctions. It contains as a particular case the Browder-Minty theorem on variational inequalities governed by monotone operators and, on the other side, Ky Fan’s minimax theorem. The main results obtained are applied to the so-called mixed equilibrium problem given by a sum of trifunctions. As an application, the authors prove the existence of a saddle point for a monotone bifunction with convexity properties only in one of the arguments. Some applications for variational inequalities are also given.
Reviewer: Samir Kumar Neogy (New Delhi)
MSC:
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
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