Monotone type operators in nonreflexive Banach spaces

Let E be a real Banach space, be the dual space of E, be the dual space of . Let be a monotone type mapping. In this paper, first, we introduce the special case when T is the weak* sub-differential of a convex function ϕ and obtain a surjective result for the mapping , where . Second, we show the existence of solutions of the variational inequality problems for strictly quasi-monotone operators and semi-monotone operators. Finally, we construct a degree theory for mappings of the class and then construct a generalized degree for the weak* sub-differential of a convex function.