A new approximation of solutions of variational inequalities for Lipschitzian monotone mappings in Hilbert Spaces

摘要

We first introduce an iterative algorithm for finding solutions of variational inequalities for Lipschitzian and monotone mappings in Hilbert spaces, and then prove a strong convergence theorem by using the modified algorithm. As its application, we deduce a strong convergence theorem for Lipschitzian and pseudo-contractions in Hilbert spaces. The results presented in this paper extend several known results.