 
Summary: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 107, No. 3, pp. 547557, DECEMBER 2000
System of Vector Equilibrium Problems
and Its Applications1
Q. H. ANSARI,2
S. SCHAIBLE,3
AND J. C. YAO
4
Abstract. In this paper, we introduce a system of vector equilibrium
problems and prove the existence of a solution. As an application, we
derive some existence results for the system of vector variational
inequalities. We also establish some existence results for the system of
vector optimization problems, which includes the Nash equilibrium
problem as a special case.
Key Words. System of vector equilibrium problems, system of vector
variational inequalities, system of vector optimization problems, Nash
equilibrium problem, fixed points.
1. Introduction and Preliminaries
In 1980, Giannessi (Ref. 1) extended classical variational inequalities
to the case of vectorvalued functions. Meanwhile, vector variational
inequalities have been researched quite extensively; for example, see Ref. 2
