Generalized Equilibrium Problems

Mircea Balaj () and Dan Florin Serac
Additional contact information
Mircea Balaj: Department of Mathematics, University of Oradea, 410087 Oradea, Romania
Dan Florin Serac: Department of Mathematics, University of Oradea, 410087 Oradea, Romania

Mathematics, 2023, vol. 11, issue 9, 1-11

Abstract: If X is a convex subset of a topological vector space and f is a real bifunction defined on X × X , the problem of finding a point x 0 ∈ X such that f ( x 0 , y ) ≥ 0 for all y ∈ X , is called an equilibrium problem. When the bifunction f is defined on the cartesian product of two distinct sets X and Y we will call it a generalized equilibrium problem. In this paper, we study the existence of the solutions, first for generalized equilibrium problems and then for equilibrium problems. In the obtained results, apart from the bifunction f , another bifunction is introduced, the two being linked by a certain compatibility condition. The particularity of the equilibrium theorems established in the last section consists of the fact that the classical equilibrium condition ( f ( x , x ) = 0 , for all x ∈ X ) is missing. The given applications refer to the Minty variational inequality problem and quasi-equilibrium problems.

Keywords: generalized equilibrium problem; equilibrium problem; fixed point; variational inequality; quasi-equilibrium problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/9/2146/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/9/2146/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:9:p:2146-:d:1138725

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().