Abstract

Using a new nonlinear mapping called generalized demimetric and the C-Q method, we first prove a strong convergence theorem for finding a fixed point for the mapping in a Banach space which generalizes simultaneously the results by Nakajo and Takahashi [Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372–379], and Solodov and Svaiter [Forcing strong convergence of proximal point iterations in a Hilbert space, Math. Programming Ser. A 87 (2000) 189–202] in a Hilbert space. Furthermore, using the mapping and the shrinking projection method, we prove another strong convergence theorem in a Banach space. We apply these results to obtain new strong convergence theorems in a Hilbert space and a Banach space.

Author information

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

Wataru Takahashi

Center for Fundamental Science, Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
and: Keio Research and Education Center for Natural Sciences, Keio University, Kouhoku-ku, Yokohama 223-8521, Japan
and: Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan

wataru@is.titech.ac.jp

Keywords

  • Fixed point
  • demimetric mapping
  • maximal monotone operator
  • metric resolvent
  • metric projection
  • hybrid method
  • shrinking projection method
  • duality mapping

Mathematics Subject Classification

47H05, 47H10

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Suggested citation

W. Takahashi. “Strong Convergence Theorems by Hybrid Methods for New Demimetric Mappings in Banach Spaces.” Journal of Convex Analysis 26 (2019), No. 1, 201–216. https://doi.org/10.68381/jca26012

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press.