Hybrid steepest iterative algorithm for a hierarchical fixed point problem

Abstract The purpose of this work is to introduce and study an iterative method to approximate solutions of a hierarchical fixed point problem and a variational inequality problem involving a finite family of nonexpansive mappings on a real Hilbert space. Further, we prove that the sequence generated by the proposed iterative method converges to a solution of the hierarchical fixed point problem for a finite family of nonexpansive mappings which is the unique solution of the variational inequality problem. The results presented in this paper are the extension and generalization of some previously known results in this area. An example which satisfies all the conditions of the iterative method and the convergence result is given.