Accelerated Krasnoselski-Mann type algorithm for hierarchical fixed point and split monotone variational inclusion problems in Hilbert spaces

Abstract

In this paper, a new accelerated extrapolation Krasnoselski-Mann type algorithm for finding common element in the solution set of the hierarchical fixed point and split monotone variational inclusion problems are introduced in the setting of a real Hilbert space. We then prove that a sequence generated by the algorithm converges strongly to such common element which also approximates solution of some fixed point problem of demimetric mapping in the space. Finally, some applications and numerical experiment are given to show effectiveness of the proposed algorithm over the recently known related results in the literature. The established results extend and generalize many recent ones announced in the literature.