In this paper, we propose a new algorithm for solving the split common fixed point problem for infinite families of demicontractive mappings. Strong convergence of the proposed method is established under suitable control conditions. We apply our main results to study the split common null point problem, the split variational inequality problem, and the split equilibrium problem in the framework of a real Hilbert space. A numerical example supporting our main result is also given.

中文翻译：

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无穷缩缩映射族的分裂公共不动点问题。

在本文中，我们提出了一种新的算法，用于解决无穷微缩压缩映射族的分裂公共不动点问题。在适当的控制条件下，该方法具有很强的收敛性。我们将主要结果用于研究实希尔伯特空间框架中的分裂公共零点问题，分裂变分不等式问题和分裂平衡问题。还给出了一个支持我们的主要结果的数值示例。