On the Existence Theorems of Equilibrium and Quasi-Equilibrium Problems in Different Spaces
Mathematics, vol.13, no.4, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 13 Issue: 4
- Publication Date: 2025
- Doi Number: 10.3390/math13040564
- Journal Name: Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
- Keywords: cyclically antimonotone, cyclically monotone, equilibrium problem, quasi-equilibrium problem, reflexive Banach space, sequentially weakly lower semicontinuous, transfer lower continuous, transfer weakly lower continuous, triangle inequality property
- Open Archive Collection: Article
- Azerbaijan State University of Economics (UNEC) Affiliated: No
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.