Journal of Convex Analysis 16 (2009), No. 3, 791--806
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 152-8552, Japan
inoue.g.aa@m.titech.ac.jp
Wataru Takahashi
Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan
wataru@is.titech.ac.jp
Kei Zembayashi
Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, 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.
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