
Journal of Convex Analysis 16 (2009), No. 3, 791806 Copyright Heldermann Verlag 2009 Strong Convergence Theorems by Hybrid Methods for Maximal Monotone Operators and Relatively Nonexpansive Mappings in Banach Spaces Go Inoue Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 1528552, Japan inoue.g.aa@m.titech.ac.jp Wataru Takahashi Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 1528552, Japan wataru@is.titech.ac.jp Kei Zembayashi Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 1528552, Japan zemba3@is.titech.ac.jp We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a relatively nonexpansive mapping in a Banach space by using two hybrid methods. Using these results, we obtain new convergence results for resolvents of maximal monotone operators and relatively nonexpansive mappings in Banach spaces. [ Fulltextpdf (142 KB)] for subscribers only. 