On generalized variational-like inequalities with generalized monotone multivalued mappings

Let E be a reflexive Banach space with the dual space E* and K be a nonempty closed convex subset of E. Let us have Psi : K x K x E* -> R and A : E* -> E*. We introduce the class of generalized alpha-monotone multifunctions T : K -> 2(E)* with respect to Psi and A where alpha : E x E -> R. By using the KIN technique and the concept of the Hausdorff metric, we establish some existence results for generalized variational-like inequalities with generalized monotone multivalued mappings in E. (C) 2008 Elsevier Ltd. All rights reserved.