Abstract
In this paper, we give a graphical version of the Ekeland’s variational principle (EVP) for equilibrium problems on weighted graphs. This version generalizes and includes other equilibrium types of EVP such as optimization, saddle point, fixed point and variational inequality ones. We also weaken the conditions on the class of bifunctions for which the variational principle holds by replacing the strong triangle inequality property by a below approximation of the bifunctions.
| Original language | English |
|---|---|
| Pages (from-to) | 33-40 |
| Number of pages | 8 |
| Journal | Proceedings of the American Mathematical Society, Series B |
| Volume | 9 |
| DOIs | |
| State | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2022 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0).
Keywords
- Ekeland variational principle
- equilibrium problem
- fixed point
- weighted graph
ASJC Scopus subject areas
- Algebra and Number Theory
- Analysis
- Discrete Mathematics and Combinatorics
- Geometry and Topology