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

Truong Minh Tuyen (), Nguyen Thi Thu Thuy () and Nguyen Minh Trang ()
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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

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 1, No 14, 291 pages

Abstract: 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.

Keywords: Split common null point problem; Monotone operator; Metric projection; Nonexpansive mapping; 47H05; 47H09; 49J53; 90C25 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01523-w

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