Abstract:
We present aunified approach for studying vector variational
inequality problems in finite dimensional spaces .We introduce
aclass of week normal mapping by virtue of the vector – valued
indicator function . Anew differential inverse variational
inequality is introduced and studied in finite dimensional
Euclidean spaces . Some result concerned with the liner growth
solution set for the differential inverse variational inequalities are
obtained under different conditions .We develop a theory of
variational inequality for demicontinuous S-contractive maps in
reflexive smooth Banach spaces . We obtain some gap functions
for generalized mixed quasi- variational inequality problems
interms of regularized gap function and D-Gap function