Summary: Journal of Global Optimization 22: 316, 2002.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
The system of generalized vector equilibrium
problems with applications
QAMRUL HASAN ANSARI1
, SIEGFRIED SCHAIBLE2
and JEN-CHIH YAO3
1Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India (E-mail:
firstname.lastname@example.org); 2A.G. Anderson Graduate School of Management, University of
California 92521-0203, USA (E-mail: email@example.com); 3Department of Applied
Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 80424, ROC (E-mail:
Abstract. In this paper, we introduce the system of generalized vector equilibrium problems which
includes as special cases the system of generalized implicit vector variational inequality problems,
the system of generalized vector variational and variational-like inequality problems and the system
of vector equilibrium problems. By using a maximal element theorem, we establish existence results
for a solution of these systems. As an application, we derive existence results for a solution of a more
general Nash equilibrium problem for vector-valued functions.
Key words: Vector equilibrium problem, Vector variational inequality, Vector optimization problem,