# Variational inequalities on Hilbert $C^*$-modules

Document Type : Research Paper

Authors

1 Department of Mathematics, Shahid Beheshti University, Tehran, Iran

2 Department of Mathematics, Shahid Beheshti University, Tehran, Iran; Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701, USA

Abstract

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