Variational inequalities on Hilbert C^*-modules

We introduce variational inequality problems on Hilbert C^*-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, C^*-valued metric projection and fixed point theory  on  Hilbert C^*-modules is studied.

Keywords:

variational inequality , Hilbert C^*-module , metric projection , Fixed point