A generalization of Ekeland’s variational principle by using the τ-distance with its applications

Abstract

Abstract In this paper, a new version of Ekeland’s variational principle by using the concept of τ-distance is proved and, by applying it, an approximate minimization theorem is stated. Moreover, by using it, two versions of existence results of a solution for the equilibrium problem in the setting of complete metric spaces are investigated. Finally some examples in order to illustrate the results of this note are given.

Keywords

• τ-distance
• Ekeland’s variational principle
• equilibrium problem
• bounded below
• lower semicontinuous function