GENERALIZED SET-VALVED STRONGLY NONLINEAR VARIATIONAL INEQUALITIES IN BANACH SPACES Cho, Y.J.; Fang, Y.P.; Huang, N.J.; Kim, K.H.;
In this paper, we introduce and study a new class of generalized strongly nonlinear variational inequalities with setvalued mappings. By using the KKM technique, we prove the existence and uniqueness of solution for this class of generalized setvalued strongly nonlinear variational inequalities in reflexive Banach spaces. Our results include the main results of Verma ［16］, ［17］ as special cases.
strongly nonlinear variational inequality;set valued-mapping;generalized monotone type mapping;generalized Lipschitzian type mapping;the KKm mapping;