International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 4, Pages 199-207

Nonlinear variational inequalities on reflexive Banach spaces and topological vector spaces

Zeqing Liu,1 Jeong Sheok Ume,2 and Shin Min Kang3

1Department of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, China
2Department of Applied Mathematics, Changwon National University, Changwon 641-773, Korea
3Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Chinju 660-701, Korea

Received 8 June 2002

Copyright © 2003 Zeqing Liu 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.


The purpose of this paper is to introduce and study a class of nonlinear variational inequalities in reflexive Banach spaces and topological vector spaces. Based on the KKM technique, the solvability of this kind of nonlinear variational inequalities is presented. The obtained results extend, improve, and unify the results due to Browder, Carbone, Siddiqi, Ansari, Kazmi, Verma, and others.