Regularized first-order methods for monotone variational inequalities with generalized projection operators

For a certain class of Banach spaces, variational inequalities with monotone operators are examined under the assumption that the data are given approximately. Regularized first-order methods (a continuous and an iterative one) are constructed in the form of equations containing generalized projection operators. Sufficient conditions are obtained for the strong convergence of these methods to the normal solution of the original problem.