Journal of Inequalities and Applications
Volume 2 (1998), Issue 1, Pages 71-87

Generalized variational inequalities of the Hartman–Stampacchia–Browder type

Sehie Park1 and Ming-Po Chen2

1Department of Mathematics, Seoul National University, Seoul 151;742, Korea
2Institute of Mathematics, Academia Sinica, Nankang, Taipei 11529, Taiwan

Received 11 December 1996

Copyright © 1998 Sehie Park and Ming-Po Chen. 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.


We obtain several generalized variational inequalities from an equilibrium theorem due to the first author under more weaker hypothesis and in more general setting than known ones. Our new results extend, unify and improve many known Hartman–Stampacchia–Browder type variational inequalities for u.s.c. or monotone type multimaps. Our proofs are also much simpler than known ones.