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.
Highlights
Ekeland’s variational principle was first expressed by Ekeland [, ] and developed by many authors and researchers
In, Bianchi et al [ ] introduced a vector version of Ekeland’s principle for equilibrium problems. They studied bifunctions defined on complete metric spaces with values in locally convex spaces ordered by closed convex cones and obtained some existence results for vector equilibria in compact and noncompact domains
The purpose of this paper is to study equilibrium problem to get some existence results
Summary
Ekeland’s variational principle was first expressed by Ekeland [ , ] and developed by many authors and researchers. Over the last few years, several authors have studied Ekeland’s variational principle for equilibrium problems under different conditions; see, for instance, [ , ]. The authors studied the equilibrium version of Ekeland’s variational principle to get some existence results for equilibrium problems in both compact and noncompact domains.
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