Bulletin of the
Korean Mathematical Society BKMS

In this paper, we propose a sufficient condition for the existence of solutions to general variational inequality problems $(GVI(K, F$, $ g))$. The condition is also necessary when $F$ is a $g$-$P_*^M$ function. We also investigate the boundedness of the solution set of $(GVI(K, F, g))$. Furthermore, we show that when $F$ is norm-coercive, the general complementarity problems $(GCP(K, F, g))$ has a nonempty compact solution set. Finally, we establish some existence theorems for $(GNCP(K, F, g))$.

Keywords: general variational inequality problem, general complementarity problem, existence, boundedness, strict feasibility, quasi-$g$-$P_*^M$ function

MSC numbers: 39B62, 47J20, 58E35, 65K10