
Journal of Convex Analysis 11 (2004), No. 1, 069080 Copyright Heldermann Verlag 2004 Strong Convergence Theorems for Nonexpansive NonselfMappings and InverseStronglyMonotone Mappings Hideaki Iiduka Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, OhOkayama, Meguroku, Tokyo 1528522, Japan, Hideaki.Iiduka@is.titech.ac.jp Wataru Takahashi Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, OhOkayama, Meguroku, Tokyo 1528522, Japan, Wataru@is.titech.ac.jp We introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive nonselfmapping and the set of solutions of the variational inequality for an inverersestronglymontone 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 inversestronglymontone 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. Keywords: Metric projection, inversestronglymonotone mapping, nonexpansive nonselfmapping, variational inequality, strong convergence. FullTextpdf (320 KB) for suscribers only. 