Solving Equilibrium Problems with Bifunctions Having the Property of Negative Transitivity. (17th February 2022)

• Record Type: Journal Article
• Authors: Balaj, Mircea
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 3(2022)
• Page Start: 307
• Page End: 321
• Publication Date: 2022-02-17
• Subjects: Equilibrium problem -- quasi-equilibrium -- the property of negative transitivity -- vector equilibrium problem; 49J53 -- 49J40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2026958
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, we introduce the notion of bifunction with the property of negative transitivity and, using the Berge-Klee intersection theorem, we establish existence theorems of the solutions for the equilibrium problems, when the involved bifunction has this property. Then, using standard scalarization techniques, we obtain existence criteria of the solutions for vector equilibrium problems. The last section of the article is devoted to the scalar and vector quasi-equilibrium problems.