Strong convergence of a modified iterative algorithm for hierarchical fixed point problems and variational inequalities

This article aims to deal with a new modified iterative projection method for solving a hierarchical fixed point problem. It is shown that under certain approximate assumptions of the operators and parameters, the modified iterative sequence {x(n)} converges strongly to a fixed point x* of T, also the solution of a variational inequality. As a special case, this projection method solves some quadratic minimization problem. The results here improve and extend some recent corresponding results by other authors.