This paper deals with a strong convergence theorem for a hybrid iterative algorithm without extrapolating step to approximate a common solution of monotone variational inclusion and hierarchical fixed point problems for nonexpansive mappings. Some consequences of the strong convergence theorem are also derived. An application to mixed equilibrium problem is also discussed. Finally, we give a numerical example to justify the main result. The method and results presented in this paper generalize and unify previously known corresponding results of this area.

中文翻译：

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求解单调变分包含和层次不动点问题的混合迭代算法

本文针对混合迭代算法处理了一个强收敛定理，而无需外推步骤来近似非膨胀映射的单调变分包含和分层不动点问题的通用解。还得出了强收敛定理的一些结果。还讨论了在混合平衡问题上的一个应用。最后，我们给出一个数值示例来证明主要结果。本文介绍的方法和结果可以概括并统一该领域以前已知的相应结果。