Approximation Iterative Algorithms of Variational Inequalities with Monotone Mapping in Infinite Dimensional Hillbert Space

A class of variational inequalities with monotone type is studied in infinite dimensional Hillbert space. By using the auxiliary variational inequality technique, the problem for solving variational inequalities with monotone mapping is transferred to solving variational inequalities with strongly monotone mapping. By constructing a new iterative algorithm, it is proved that iterative sequence generated by the new algorithm converge strongly to the solutions of variational inequalities with monotone mapping. The results generalizes many important results in literature.