In this paper, we present a modified SP iteration with the inertial technical term for three quasi-nonexpansive multivalued mappings in a Hilbert space. We then obtain weak convergence theorem under suitable conditions. The strong convergence theorems are given using CQ and shrinking projection methods with our modified iteration. Finally, we test some numerical experiments to illustrate that our inertial forward–backward method with the inertial technique term has a more effective convergence than that of the standard forward–backward method and Halpern algorithm.

中文翻译：

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希尔伯特空间中拟非扩张多值映象的带SP迭代的改进混合投影方法

在本文中，我们针对Hilbert空间中的三个拟非膨胀多值映射，提供了一个具有惯性技术术语的改进的SP迭代。然后，我们在适当的条件下获得弱收敛定理。通过改进的迭代，使用CQ和收缩投影方法给出了强收敛定理。最后，我们测试了一些数值实验，以证明我们的惯性前后方法与惯性技术项相比，具有比标准前进和后退方法和Halpern算法更有效的收敛性。