Summary: Nonlinear Analysis 61 (2005) 119
Existence results for Stampacchia and Minty type
implicit variational inequalities with multivalued
, M.F. Yanga
, Q.H. Ansarib,1
, G. Kassayc,2
aDepartment of Mathematics, National Changhua University of Education, Changhua, Taiwan 50058,
Republic of China
bDepartment of Mathematical Sciences, King Fahd University of Petroleum and Minerals, P.O. Box 1169,
Dhahran 31261, Saudi Arabia
cDepartment of Mathematics, Eastern Mediterranean University, TRNC, Gazi Magusa, Mersin 10, Turkey
Received 4 December 2003; accepted 27 July 2004
Stampacchia and Minty type generalized implicit variational inequality problems are considered.
We extended the notion of dense pseudomonotonicity for multivalued maps and established several
existence results for solutions of these problems in the setting of segment-dense sets. We also studied
the existence of solutions of Minty type generalized implicit quasi-variational inequality problems.