Strong Convergence Theorems for Nonexpansive Nonself-Mappings and Inverse-Strongly-Monotone Mappings

We introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive nonself-mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common element of the set of zeros of a maximal montone mapping and the set of zeros of an inverse-strongly-montone mapping and the problem of finding a common element of the closed convex set and the set of zeros of the gradient of a continuously Frechet differentiable convex functional.