On the generalized monotonicity of variational inequalities

In this paper, three new classes of generalized monotone operators are introduced: the relaxed μμ pseudomonotone operator, relaxed μμ quasimonotone operator and densely relaxed pseudomonotone operator. The relations between these three classes and the relations between them and some other well known classes of generalized monotone operators are discussed in detail. Various existence results for variational inequalities in normed spaces are derived. The results generalize some known results.