Journal of Inequalities and Applications 
Volume 3 (1999), Issue 2, Pages 161-181
doi:10.1155/S1025583499000120

A study of variational inequalities for set-valued mappings

Kok-Keong Tan,1 Enayet Tarafdar,2 and George Xian-Zhi Yuan2

 1Department of Mathematics, Statistics and CS, Dalhousie University, Halifax B3H 3J5, Canada
2Department of Mathematics, The University of Queensland, Brisbane 4072, Australia
Received 27 November 1997; Revised 14 February 1998

Abstract

In this paper, Ky Fan’s KKM mapping principle is used to establish the existence of solutions for simultaneous variational inequalities. By applying our earlier results together with Fan–Glicksberg fixed point theorem, we prove some existence results for implicit variational inequalities and implicit quasi-variational inequalities for set-valued mappings which are either monotone or upper semi-continuous.