In this paper, we introduce a modified Krasnoselski–Mann type method for solving the hierarchical fixed point problem and split monotone variational inclusions in real Hilbert spaces. We prove that the sequence generated by the modified algorithm converges strongly to a common element of the set of hierarchical fixed point problem and split monotone variational inclusions only basing on the coefficients. Our results extend and improve the weak convergence results of Kazmi et al. (Kazmi et al., 2018) and others. Moreover, an application and its numerical examples illustrate the feasibility and strong convergence of the proposed method and results.

在本文中，我们介绍了一种改进的Krasnoselski–Mann型方法，用于解决分层的不动点问题和实希尔伯特空间中的分裂单调变分包含。我们证明了由改进算法生成的序列强烈收敛到层次不动点问题集的一个公共元素，并且仅基于系数分裂了单调变分包含。我们的结果扩展并改善了Kazmi等人的弱收敛结果。（Kazmi et al。，2018）等。此外，一个应用程序及其数值示例说明了该方法和结果的可行性和强收敛性。