Abstract
In this paper, we consider the system of vector quasi-equilibrium problems with or without involving φ-condensing maps and prove the existence of its solution. Consequently, we get existence results for a solution to the system of vector quasi-variational-like inequalities. We also prove the equivalence between the system of vector quasi-variational-like inequalities and the Debreu type equilibrium problem for vector-valued functions. As an application, we derive some existence results for a solution to the Debreu type equilibrium problem for vector-valued functions.
| Original language | English |
|---|---|
| Pages (from-to) | 45-57 |
| Number of pages | 13 |
| Journal | Journal of Global Optimization |
| Volume | 29 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 May 2004 |
Keywords
- φ-condensing maps
- Debreu type equilibrium problem
- Maximal element theorem
- Partial gâteaux derivative
- System of vector quasi-equilibrium problems
- System of vector quasi-variational-like inequalities
ASJC Scopus subject areas
- Computer Science Applications
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics