Convergence Theorems for Hierarchical Fixed Point Problems and Variational Inequalities

This paper deals with a modified iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under certain approximate assumptions of mappings and parameters. As a special case, this projection method solves some quadratic minimization problem. It should be noted that the proposed method can be regarded as a generalized version of Wang and Xu (2013), Ceng et al. (2011), Sahu et al. ( 2012), and many other authors.