A generalization of Ekeland’s variational principle by using the τ -distance and its application in equilibrium problem

In this paper, a new version of Ekeland's variational principle by using the concept of \tau-distance for bounded from below functions which are not necessarily lower semicontinuous is provided. This new version of Ekeland's variational principle will be applied to establish an existence theorem for a solution to the equilibrium problem in the setting of complete metric spaces.

Keywords:

Lower semicontinuous Regularization , Ekeland’s variational principle , Bounded from below , equilibrium problem , τ -distance