Existence theorems of generalized quasi-variational inequalities with upper hemi-continuous and demi operators on non-compact sets
Mohammad S. R. Chowdhury, E Tarafdar · Mathematical Inequalities & Applications · 1999
Suppose that E is a topological vector space and X is a non-empty subset of E . Let S : X 2 X and T : X 2 E * be two maps. Then the generalized quasi-variational inequality problem (GQVI) is to find a point S( ) and a point T( ) such that Re , x 0 for all x S( ) . We shall use Chowdhury and Tan's generalized version [4] of Ky Fan's minimax inequality We obtain the existence theorems of GQVI on paracompact sets X where the set-valued operators T are demi operators [3] and are upper hemi-continuous [5] along line segments in X to the weak * -topology on E * .