Some resolvent iterative methods for variational inclusions and nonexpansive mappings

In this paper, we suggest and analyze three-step iterations for finding the common element of the set of fixed points of a nonexpansive mappings and the set of the solutions of the variational inclusions using the resolvent operator technique. We also study the convergence criteria of three-step iterative method under some mild conditions. Our results include the previous results of Noor [M. Aslam Noor, General variational inequalities and nonexpansive mappings, J. Math. Anal. Appl. 331 (2007) 810–822] and Noor and Huang [M. Aslam Noor, Zhenyu Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput., in press. http://dx.doi.org/10.1016/j.amc.2006.08.088] as special cases and may be considered as an improvement and refinement of the previously known results.