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- Title
Graphical Ekeland’s variational principle with a generalized ພ-distance and a new approach to quasi-equilibrium problems.
- Authors
CHAIPUNYA, PARIN; CHUENSUPANTHARAT, NANTAPORN; SANGUANSUTTIGUL, PRINTAPORN
- Abstract
In this paper, we introduce the generalized Ekeland’s variational principle in several forms. The general setting of our results includes a graphical metric structure and also employs a generalized ພ-distance. We then applied the proposed variational principles to obtain existence theorems for a class of quasi-equilibrium problems whose constraint maps are induced from the graphical structure. The conditions used in our existence results are based on a very general concept called a convergence class. Finally, we deduce the existence of a generalized Nash equilibrium via its quasi-equilibrium reformulation. A validating example is also presented.
- Subjects
VARIATIONAL principles; QUASI-equilibrium; NASH equilibrium; EXISTENCE theorems
- Publication
Carpathian Journal of Mathematics, 2023, Vol 39, Issue 1, p95
- ISSN
1584-2851
- Publication type
Article
- DOI
10.37193/CJM.2023.01.06