Abstract

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

Author information

Contact details are reproduced from the original publication and may be historical.

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

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Suggested citation

G. Inoue, W. Takahashi, K. Zembayashi. “Strong Convergence Theorems by Hybrid Methods for Maximal Monotone Operators and Relatively Nonexpansive Mappings in Banach Spaces.” Journal of Convex Analysis 16 (2009), No. 3&4, 791–806. https://doi.org/10.68381/jca16048

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Published by Heldermann Verlag, 2009. Rights now held by Banach Press LLC.