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A Strong Convergence Theorem for a Parallel Iterative Method for Solving the Split Common Null Point Problem in Hilbert Spaces

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Abstract

There are many iterative methods for solving the split common null point problems involving step sizes that depend on the norm of a bounded linear operator T. We know that the implementation of such algorithms is usually difficult to handle, because we have to compute the norm of the operator T. So, we propose new iterative methods involving a step size selected in such a way that its implementation does not require the computation or estimation of the norm of the operator T. In this paper, a new parallel iterative method for solving the split common null point problem is introduced in Hilbert spaces, without prior knowledge of operator norms. Moreover, some applications of our main results to the multiple-set split feasibility problem and the split minimum point problem are also presented.

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Acknowledgements

The first author was supported by the Science and Technology Fund of Vietnam Ministry of Education and Training (B2019). The third author was supported by the Science and Technology Fund of Thai Nguyen University of Technology (TNUT). The authors would like to thank the referees and the editor for their valuable comments and suggestions which improve the presentation of this manuscript.

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Authors and Affiliations

  1. Thai Nguyen University of Science, Thai Nguyen, Vietnam

    Truong Minh Tuyen

  2. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam

    Nguyen Thi Thu Thuy

  3. Faculty of International Training, Thainguyen University of Technology, Thai Nguyen, Vietnam

    Nguyen Minh Trang

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  1. Truong Minh Tuyen
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  2. Nguyen Thi Thu Thuy
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  3. Nguyen Minh Trang
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Correspondence to Truong Minh Tuyen.

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Tuyen, T.M., Thuy, N.T.T. & Trang, N.M. A Strong Convergence Theorem for a Parallel Iterative Method for Solving the Split Common Null Point Problem in Hilbert Spaces. J Optim Theory Appl 183, 271–291 (2019). https://doi.org/10.1007/s10957-019-01523-w

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  • DOI: https://doi.org/10.1007/s10957-019-01523-w

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