Ekeland-type variational principles and equilibrium problems

In this survey chapter we present different forms of Ekeland’s variational principle involving τ -functions, τ -functions and fitting functions, and Q-functions, respectively. The equilibrium version of Ekeland-type variational principle is also presented. We give some equivalences of our variational principles with the Caristi- Kirk-type fixed point theorem for multivalued maps, Takahashi minimization theorem, and some other related results. As applications of our results, we derive the existence results for solutions of equilibrium problems and fixed point theorems for multivalued maps. The results of this chapter extend and generalize many results that recently appeared in the literature.