In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms. Finally, in applications, our main results in this paper are applied to signal recovery problems.

中文翻译：

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一种新的具有出色稳定性的加速自适应步长调整算法，用于分解公共不动点问题

在希尔伯特空间的框架中，我们研究了分裂公共不动点问题的解。在惯性技术和Meir-Keeler压缩映射的影响下，提出了一种新的具有出色稳定性的加速自适应步长算法。在没有算子准则的先验知识的情况下获得了强收敛定理。最后，在应用中，我们在本文中的主要结果被应用于信号恢复问题。