ABSTRACT

In this paper, we introduce a new iterative algorithm from primal-dual methods for solving the split equality common fixed-point problem of quasi-nonexpansive mappings in real Hilbert space. Our algorithm includes the simultaneous iterative algorithm as special case which has been proposed by Moudafi and Al-Shemas for solving the split equality common fixed-point problem. We use a way of selecting the stepsizes such that the implementation of our algorithm does not need any prior information about bounded linear operator norms. It avoids the difficult task of estimating the operator norms. Under suitable conditions, we get the weak convergence of the proposed algorithm. The performance of the proposed algorithm is also illustrated by preliminary numerical experiments. The results presented in the paper improve and extend some corresponding results.

摘要

在本文中，我们从原对偶方法引入了一种新的迭代算法，用于解决实希尔伯特空间中拟非扩张映射的分割等式公共不动点问题。我们的算法包括Moudafi和Al-Shemas为解决分裂等式公共不动点问题而提出的作为特殊情况的同时迭代算法。我们使用一种选择步长的方法，这样我们算法的实现就不需要关于有界线性算子范数的任何先验信息。它避免了估算运营商规范的艰巨任务。在合适的条件下，我们得到了该算法的弱收敛性。初步的数值实验也说明了该算法的性能。本文中提出的结果改进并扩展了一些相应的结果。