Hybrid viscosity approximation methods for systems of variational inequalities and hierarchical fixed point problems


Lu-Chuan Ceng, Ching-Feng Wen, Jen-Chih Yao, Yonghong Yao




In this paper, we propose an implicit iterative method and an explicit iterative method for solving a general system of variational inequalities with a hierarchical fixed point problem constraint for an infinite family of nonexpansive mappings. We show that the proposed algorithms converge strongly to a solution of the general system of variational inequalities, which is a unique solution of the hierarchical fixed point problem.