Summary: 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 the authors [J. Math. Anal. Appl. 331, No. 2, 810–822 (2007; Zbl 1112.49013
); Appl. Math. Comput. 187, No. 2, 680–685 (2007; Zbl 1128.65050
)] as special cases and may be considered as an improvement and refinement of the previously known results.