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Strong convergence theorem for a finite family of demimetric mappings with variational inequality problems in a Hilbert space

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Abstract

In this paper, using Halpern type iteration, we prove a strong convergence theorem for finding a common element of the set of common fixed points for a finite family of demimetric mappings and the set of common solutions of variational inequality problems for a finite family of inverse strongly monotone mappings in a Hilbert space. Using this result, we obtain well-known and new strong convergence theorems in a Hilbert space.

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Acknowledgements

The author was partially supported by Grant-in-Aid for Scientific Research No. 15K04906 from Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung, 80702, Taiwan

    Wataru Takahashi

  2. Keio Research and Education Center for Natural Sciences, Keio University, Kouhoku-ku, Yokohama, 223-8521, Japan

    Wataru Takahashi

  3. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, 152-8552, Japan

    Wataru Takahashi

Authors
  1. Wataru Takahashi
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Correspondence to Wataru Takahashi.

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Takahashi, W. Strong convergence theorem for a finite family of demimetric mappings with variational inequality problems in a Hilbert space. Japan J. Indust. Appl. Math. 34, 41–57 (2017). https://doi.org/10.1007/s13160-017-0237-0

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  • DOI: https://doi.org/10.1007/s13160-017-0237-0

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