Systems of unrelated generalized mixed equilibrium problems and unrelated hierarchical fixed point problems in Hilbert space

摘要

In this paper, we investigate a hybrid extra-gradient iterative method to approximate the common solution of a system of unrelated generalized mixed equilibrium problems for monotone and Lipschitz continuous mappings and system of unrelated hierarchical fixed point problems for nonexpansive mappings in Hilbert space.We prove a strong convergence theorem for the sequences generated by the proposed iterative algorithm.Further, we give some consequences and applications of our main result.Finally, we discuss a numerical example to demonstrate the applicability of the iterative algorithm.