Abstract
Nonexpansive mappings and inverse-strongly monotone mappings are two kinds of nonlinear operators, nonlinear functional analysis. Operator theory is a very important theory, which has some valuable applications to operations research and economics. It has recently been applied to engineering, particularly in the application of automatic control. In this paper, we introduce an iterative method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an alpha inverse-strongly monotone mapping in Hilbert space. We obtain a strong convergence theorem for a sequence generated by this progress.
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