International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 637-642

A general vector-valued variational inequality and its fuzzy extension

Sehie Park,1 Byung-Soo Lee,2 and Gue Myung Lee3

1Department of Mathematics, Seoul National University, Seoul 151-742, Korea
2Department of Mathematics, Kyungmng University, Pusan 608-736, Korea
3Department of Applied Mathematics, Pukyong National University, Pusan 608-737, Korea

Received 12 December 1996

Copyright © 1998 Sehie Park 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.


A general vector-valued variational inequality (GVVI) is considered. We establish the existence theorem for (GVVI) in the noncompact setting, which is a noncompact generalization of the existence theorem for (GVVI) obtained by Lee et al., by using the generalized form of KKM theorem due to Park. Moreover, we obtain the fuzzy extension of our existence theorem.