A Strong Convergence Theorem for a Parallel Iterative Method for Solving the Split Common Null Point Problem in Hilbert Spaces
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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.
KeywordsSplit common null point problem Monotone operator Metric projection Nonexpansive mapping
Mathematics Subject Classification47H05 47H09 49J53 90C25
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.
- 24.Tuyen, T.M., Ha, N.S., Thuy, N.T.T.: A shrinking projection method for solving the split common null point problem in Banach spaces. Numer. Algorithms https://doi.org/10.1007/s11075-018-0572-5 (2018)