We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we show that a sequence generated by the algorithm converges strongly to common solution. Furthermore, we list some consequences of our established theorem. Finally, we provide a numerical example to demonstrate the applicability of the algorithm. We emphasize that the result accounted in manuscript unifies and extends various results in this field of study.

中文翻译：

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分裂单调变分包含，变分不等式和不动点问题的迭代方案

我们提出并分析一种新型的迭代算法，以在Hilbert空间的框架中为无限的非膨胀映射族找到分裂单调变分包含，变分不等式和不动点问题的通用解。此外，我们证明了该算法生成的序列强烈收敛于公共解。此外，我们列出了已建立定理的一些结果。最后，我们提供了一个数值例子来说明该算法的适用性。我们强调在手稿中说明的结果统一并扩展了该研究领域中的各种结果。