Asymptotic Analysis with Deferential Inverse and Variational inequality with Gap function

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