In this paper, we investigate the generalized Halpern iteration for computing fixed points of nonexpansive mappings in Hilbert space setting, and prove the strong convergence under new control conditions on parameters. The convergence results generalize the existing ones in the literature. We also present a convergence rate analysis for the generalized Halpern iteration with a particular choice of parameters. Finally, we give an application to the split feasibility problem and two numerical examples for illustrating the performance of the algorithm.

中文翻译：

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新控制条件下的广义Halpern迭代及其应用

在本文中，我们研究了用于计算 Hilbert 空间设置中非扩展映射的不动点的广义 Halpern 迭代，并证明了在新的参数控制条件下的强收敛性。收敛结果概括了文献中现有的结果。我们还对具有特定参数选择的广义 Halpern 迭代进行了收敛率分析。最后，我们给出了分裂可行性问题的应用和两个数值例子来说明算法的性能。