Document Type : Research Paper
Department of Mathematics, Shahid Beheshti University, Tehran, Iran
Department of Mathematics, Shahid Beheshti University, Tehran, Iran; Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701, 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.