Abstract
In this paper, we introduce systems of simultaneous generalized vector equilibrium problems and prove the existence of their solutions. As application of our results, we derive the existence theorems for solutions of systems of vector saddle-point problems. Consequently, we prove the existence of a solution of systems of generalized minimax inequalities. Further application of our results is also given to establish the existence of a solution of a Debreu-type equilibrium problem for vector-valued functions.
| Original language | English |
|---|---|
| Pages (from-to) | 27-44 |
| Number of pages | 18 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 127 |
| Issue number | 1 |
| DOIs | |
| State | Published - Oct 2005 |
Bibliographical note
Funding Information:1The first author thanks the Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities. The second and third authors were supported by the National Science Council of the Republic of China. The authors are grateful to the referees for valuable suggestions and comments. 2Associate Professor, Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahrau Saudi Arabia; on leave from Department of Mathematics, Aligarh Muslim University, Aligarh, India. 3Professor, Department of Mathematics, National Changhua University of Education, Changhua, Taiwan, ROC. 4Research Student, Department of Mathematics, National Changhua University of Education, Changhua, Taiwan, ROC.
Keywords
- Debreu-type equilibrium problems
- Properly convex functions
- Systems of minimax inequalities
- Systems of simultaneous generalized vector equilibrium problems
- Systems of vector saddle point problems
ASJC Scopus subject areas
- Management Science and Operations Research
- Control and Optimization
- Applied Mathematics