The purpose of this paper is to introduce and study the existence problem of solution for a system of monotone variational inclusion problems in Hilbert spaces. By using the inertial forward-backward splitting technique, we propose and analyze an algorithm. Under suitable conditions, we proved that the sequence generated by the algorithm converges strongly to a solution of such kind of monotone variational inclusion problems. At the end of the paper, some applications are also given. The results presented in the paper extend and improve some recent results.

中文翻译：

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求解希尔伯特空间中包含问题系统的惯性前向后向分裂技术

本文的目的是介绍和研究希尔伯特空间中一个单调变分包含问题系统的解存在性问题。通过使用惯性前向后向分裂技术，我们提出并分析了一种算法。在合适的条件下，我们证明了算法生成的序列强烈收敛于此类单调变分包含问题的解。在论文的最后，还给出了一些应用。论文中提出的结果扩展并改进了一些最近的结果。