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The split common null point problem for generalized resolvents in two banach spaces

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Abstract

In this paper, we consider the split common null point problem in two Banach spaces. Then, using the generalized resolvents of maximal monotone operators and the generalized projections, we prove a strong convergence theorem for finding a solution of the split common null point problem in two Banach spaces. It seems that such a theorem for generalized resolvents is the first of its kind outside Hilbert spaces.

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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

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  1. Wataru Takahashi
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Correspondence to Wataru Takahashi.

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Takahashi, W. The split common null point problem for generalized resolvents in two banach spaces. Numer Algor 75, 1065–1078 (2017). https://doi.org/10.1007/s11075-016-0230-8

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  • DOI: https://doi.org/10.1007/s11075-016-0230-8

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