Modified Krasnoselski-Mann type iterative algorithm with strong convergence for hierarchical fixed point problem and split monotone variational inclusions

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. (c) 2021 Elsevier B.V. All rights reserved.