Systems of generalized variational inequalities and their applications^∗

^∗This research war supported by the National Science Council of the Republic of China.

Abstract

In this paper, we first introduce the system of generalized implicit variational inequalities and prove the existence of its solution. Then we derive existence results for systems of generalized variational and variational like inequalities and system of variational inequalities. As applications, we establish some existence results for a solution to the system of optimization problems which includes the Nash equilibrium problem as a special case

Keywords:

• The system of generalized implicit variational inequalities
• the system of generalized variational like inequalities
• the system of variational inequalities
• the system of optimization problems
• the Nash equilibrium problem
• fixed points

^∗This research war supported by the National Science Council of the Republic of China.

^†Present address: Department of Applied Mathematics, Natmnal Sun Yat-sen University, Kaohsiung 804, Taiwan. ROC.

^∗This research war supported by the National Science Council of the Republic of China.

^†Present address: Department of Applied Mathematics, Natmnal Sun Yat-sen University, Kaohsiung 804, Taiwan. ROC.

Notes

^∗This research war supported by the National Science Council of the Republic of China.

^†Present address: Department of Applied Mathematics, Natmnal Sun Yat-sen University, Kaohsiung 804, Taiwan. ROC.