Set-valued nonlinear variational inequalities for H-monotone mappings in nonreflexive Banach spaces Original Research Article

Let H be a mapping from a normed space X to a normed space Y. In the monograph by Vainberg Variational method and method of monotone operators, Nauka, Moskva, 1972, a mapping T from a normed space X to the dual space Y∗ of a normed space Y is said to be H-monotone if 〈Tx−Ty,H(x−y)〉⩾0,∀x,y∈X, where H is a mapping from X to Y. In nonreflexive Banach spaces nonlinear variational inequalities for upper-semi-continuous H-monotone set-valued mappings T have not been investigated yet even though this is an interesting problem. The present paper is concerned with this difficult one