On equilibrium problems

Abstract

In this chapter we give an overview of the theory of scalar equilibrium problems. To emphasize the importance of this problem in nonlinear analysis and in several applied fields we first present its most important particular cases as optimization, Kirszbraun’s problem, saddlepoint (minimax) problems, and variational inequalities. Then, some classical and new results together with their proofs concerning existence of solutions of equilibrium problems are exposed. The existence of approximate solutions via Ekeland’s variational principle - extended to equilibrium problems - is treated within the last part of the chapter.