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

摘要

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. MSC:47H10, 47J20, 47H09, 47H05.