Journal of Inequalities and Applications
Volume 3 (1999), Issue 2, Pages 161-181

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

Copyright © 1999 Kok-Keong Tan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.