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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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Listed:
  • Truong Minh Tuyen

    (Thai Nguyen University of Science)

  • Nguyen Thi Thu Thuy

    (Hanoi University of Science and Technology)

  • Nguyen Minh Trang

    (Thainguyen University of Technology)

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.

Suggested Citation

  • Truong Minh Tuyen & Nguyen Thi Thu Thuy & Nguyen Minh Trang, 2019. "A Strong Convergence Theorem for a Parallel Iterative Method for Solving the Split Common Null Point Problem in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 271-291, October.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:1:d:10.1007_s10957-019-01523-w
    DOI: 10.1007/s10957-019-01523-w
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    References listed on IDEAS

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    1. Boikanyo, Oganeditse A., 2015. "A strongly convergent algorithm for the split common fixed point problem," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 844-853.
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