- - - Department of Mathematics, Shahid Beheshti University, Tehran, Iran
- - - Department of Mathematics, Shahid Beheshti University, Tehran, Iran; Department of Mathematics, University of Arkansas, Fayetteville, Arkansas ۷۲۷۰۱, USA

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.

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