Document Type : Research Paper

Authors

• Hedayat Fathi ¹
• S.A.R. Hosseinioun ²

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

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