In this paper, we establish some existence results of the solutions for several multivalued variational inequalities involving elements belonging to a class of operators that was recently introduced in the literature. As applications weobtain some new coincidence point results in Hilbert spaces.

We give several regularity conditions, both closedness and interior point type, that ensure the maximal monotonicity of the generalized parallel sum of two maximal monotone operators of Gossez type (D), and we extend some recent results concerning on the same problem.

In this paper we show that the local monotonicity in the sense of Minty and Browder on some residual sets assure the global monotonicity and, according to an earlier result, the convexity of the inverse images. We pay some special attention to the residual sets arising as complements of some special first Baire category sets, namely the sigma-affine sets, the sigma-compact sets and the sigma-algebraic varieties. We achieve this goal gradually by

We give several regularity conditions, both closedness and interior point type, that ensure the maximal monotonicity of the generalized sum of two stronglyrepresentablemonotone operators, and we extend some recent results concerning on the same problem.