In this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem and the split equality fixed point problem of firmly quasi-nonexpansive mappings in real Hilbert spaces. Under very mild conditions, we prove a weak convergence theorem for our algorithm using projection method and the properties of firmly quasi-nonexpansive mappings. Our result improves and extends the corresponding ones announced by some others in the earlier and recent literature.

中文翻译：

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多集分割可行性问题和分割等式不动点问题的一种新的迭代算法

在本文中，我们提出了一种新的迭代算法，用于解决实希尔伯特空间中的拟集-拟非扩张映射的多集拆分可行性问题和拆分等式不动点问题。在非常温和的条件下，我们使用投影方法和稳固拟非扩张映射的性质证明了算法的弱收敛定理。我们的结果改进并扩展了其他文献在早期和最近的文献中宣布的对应文献。