Iterative methods for finding minimum-norm fixed points of nonexpansive mappings with applications

The set S of fixed points of a nonexpansive mapping T in a Hilbert space is always closed convex. Assume the set is also nonempty. It is then of interest to find the element x(dagger) of this set with least norm; that is, the minimum-norm fixed point of T. In this article we provide two methods (one implicit and one explicit) for finding x(dagger). As a matter of fact, we will consider a more general problem of finding a point (x) over tilde in S which solves a variational inequality problem. Applications to convex minimization problems and convexly constrained linear inverse problems are included.