In this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors.

中文翻译：

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Banach空间中渐近非扩张映射的分割公共不动点问题的迭代解

在本文中，我们提出了一种迭代算法，用于在两个实际Banach空间的框架中找到渐近非扩张映射的分裂公共不动点。在施加于参数序列的一些合适条件下，证明了一些强收敛定理，这些定理也解决了一些与优化问题密切相关的变分不等式。这里的结果概括并完善了其他作者的主要结果。