The purpose of the present paper is to construct a common solution of the split null point problem associated with the maximal monotone operators and the fixed point problem associated with a finite family of 𝕜-demicontractive operators in Hilbert spaces. We compute the optimal common solution via inertial parallel hybrid algorithm under a suitable set of control conditions. The viability of parallel implementation of the algorithm is demonstrated for various theoretical as well as numerical results. The results presented in this paper improve various existing results in the current literature.

中文翻译：

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希尔伯特空间中定点和分割零点问题的基于加速投影的并行混合算法

本文的目的是构建与最大单调算子相关的分割零点问题和与有限族相关的不动点问题的通用解决方案𝕜-希尔伯特空间中的半收缩算子。我们在一组合适的控制条件下通过惯性并行混合算法计算最佳公共解决方案。各种理论和数值结果证明了该算法并行实现的可行性。本文提出的结果改进了当前文献中的各种现有结果。