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Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces

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Abstract

Generalized split feasibility problems governed by generalized hybrid mappings are studied via iterative methods. Several algorithms are introduced to solve them. In particular, weak convergence of these algorithms is proved. As tools, averaged mappings and resolvents of maximal monotone operators are technically maneuvered to facilitate the argument of the proofs to the main results. Applications to Mann’s iteration method for nonexpansive mappings and to equilibrium problems are included.

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Authors and Affiliations

  1. Department of Applied Mathematics, Kaohsiung Medical University, Kaohsiung, 80424, Taiwan

    Wataru Takahashi, Hong-Kun Xu & Jen-Chin Yao

  2. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Jen-Chin Yao

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

    Wataru Takahashi

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

    Wataru Takahashi

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

    Jen-Chin Yao

Authors
  1. Wataru Takahashi
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  2. Hong-Kun Xu
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  3. Jen-Chin Yao
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Corresponding author

Correspondence to Wataru Takahashi.

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Takahashi, W., Xu, HK. & Yao, JC. Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces. Set-Valued Var. Anal 23, 205–221 (2015). https://doi.org/10.1007/s11228-014-0285-4

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  • DOI: https://doi.org/10.1007/s11228-014-0285-4

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