In this paper, we modified the shrinking projection method with the parallel monotone hybrid method for approximating common fixed points of a finite family of G-nonexpansive mappings. We then prove a strong convergence theorem under suitable conditions in Hilbert spaces endowed with graphs. Moreover, we give some numerical examples and compare the rate of convergence of our algorithms. Finally, we provide an application to signal recovery in a situation without knowing the type of noises and demonstrate the computational performance of our algorithm in comparison to some methods. The numerical results of the comparative analysis are also discussed.

中文翻译：

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Hilbert空间中$$ G-$$ G-非膨胀映射的有限族的并行单调混合算法，具有适用于信号恢复的图

在本文中，我们用并行单调混合方法对收缩投影方法进行了修改，以逼近有限个G非扩张映射的公共不动点。然后，我们在赋予图的希尔伯特空间中的适当条件下，证明了一个强收敛定理。此外，我们提供了一些数值示例，并比较了算法的收敛速度。最后，我们提供了一种在不知道噪声类型的情况下进行信号恢复的应用程序，并展示了与某些方法相比我们的算法的计算性能。还讨论了比较分析的数值结果。