Zhao Jing, Zong Haili
1Tianjin Key Lab for Advanced Signal Processing, Civil Aviation University of China, Tianjin, China.
2College of Science, Civil Aviation University of China, Tianjin, China.
J Inequal Appl. 2018;2018(1):83. doi: 10.1186/s13660-018-1668-0. Epub 2018 Apr 13.
In this paper, we propose parallel and cyclic iterative algorithms for solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators. We also combine the process of cyclic and parallel iterative methods and propose two mixed iterative algorithms. Our several algorithms do not need any prior information about the operator norms. Under mild assumptions, we prove weak convergence of the proposed iterative sequences in Hilbert spaces. As applications, we obtain several iterative algorithms to solve the multiple-set split equality problem.
在本文中，我们提出了用于求解强拟非扩张算子的多集分裂等式公共不动点问题的并行和循环迭代算法。我们还将循环迭代方法和并行迭代方法的过程相结合，提出了两种混合迭代算法。我们的几种算法不需要关于算子范数的任何先验信息。在温和的假设下，我们证明了所提出的迭代序列在希尔伯特空间中的弱收敛性。作为应用，我们得到了几种求解多集分裂等式问题的迭代算法。
