ALGORITHMS CONSTRUCTION FOR NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY MONOTONE MAPPINGS

Abstract

In this paper, we construct two algorithms for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an $\alpha$-inverse-strongly monotone mapping in a Hilbert space. We show that the sequence converges strongly to a common element of two sets under the some mild conditions on parameters. As special cases of the above two algorithms, we obtain two schemes which both converge strongly to the minimum norm element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an $\alpha$-inverse-strongly monotone mapping.