Inertial Krasnosel'skii-Mann type hybrid algorithms for solving hierarchical fixed point problems

In this paper, we suggest two inertial Krasnosel'skii-Mann type hybrid algorithms to approximate a solution of a hierarchical fixed point problem for nonexpansive mappings in Hilbert space. We prove strong convergence theorems for these algorithms and the conditions of the convergence are very weak comparing other algorithms for the hierarchical fixed point problems. Further, we derive some consequences from the main results. Finally, we present two academic numerical examples for comparing these two algorithms with the algorithm in Dong et al. (J Fixed Point Theory A 19(4):3097-3118, 2017), which illustrate the advantage of the proposed algorithms. The methods and results presented in this paper generalize and unify previously known corresponding methods and results of this area.