On the Existence Theorems of Equilibrium and Quasi-Equilibrium Problems in Different Spaces

Ali Farajzadeh (), Mahmood Ghobadi and Jen-Chih Yao ()
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Ali Farajzadeh: Department of Mathematics, Faculty of Science, Razi University, Kermanshah 67149, Iran
Mahmood Ghobadi: Department of Mathematics, Faculty of Science, Razi University, Kermanshah 67149, Iran
Jen-Chih Yao: Center for General Education, China Medical University, Taichung 404327, Taiwan

Mathematics, 2025, vol. 13, issue 4, 1-20

Abstract: In this article, the solvability of the equilibrium problem (EP), Minty equilibrium problem (MEP), and quasi-equilibrium problem (QEP) by using the notions of cyclically monotone and cyclically antimonotone in the setting of topological vector spaces and metric spaces is investigated. Also, the concepts transfer lower continuity, transfer weakly lower continuity, lower semicontinuity, from above, and sequentially weakly lower semicontinous which are weaker notions than the lower semicontinuity for establishing the existence results for EP and QEP, and the other forms of them are applied. Moreover, by using the famous results for the minimum points of a function, some existence theorems, by using the triangle property, of solutions for EP and QEP are given when the domains of bifunctions are compact and not compact. The results of this paper can be viewed as new versions of the corresponding published results with new and mild assumptions.

Keywords: equilibrium problem; quasi-equilibrium problem; transfer lower continuous; transfer weakly lower continuous; sequentially weakly lower semicontinuous; reflexive Banach space; cyclically monotone; cyclically antimonotone; triangle inequality property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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