Vector Equilibrium Problems,Minimal Element Problems and Least Element Problems

In this paper we introduce some concepts of feasible sets for vector equilibrium problems and some classes of Z-maps for vectorial bifunctions. Under strict pseudomonotonicity assumptions, we investigate the relationship between minimal element problems of feasible sets and vector equilibrium problems. By using Z-maps, we further study the least element problems of feasible sets for vector equilibrium problems. Finally, we prove a generalized sublattice property of feasible sets for vector equilibrium problems associated with Z-maps. This work was supported by the National Natural Science Foundation of China and the Applied Research Project of Sichuan Province (05JY029-009-1). The authors thank Professor Charalambos D. Aliprantis and the referees for valuable comments and suggestions leading to improvements of this paper.