  In this paper, we introduce a new iterative method to find a common solution
of a generalized mixed equilibrium problem, a variational inequality problem
and a hierarchical fixed point problem for a demicontinuous nearly nonexpansive
mapping. We prove that the proposed method converges strongly to a common
solution of above problems under the suitable conditions. It is also noted that
the main theorem is proved without usual demiclosedness condition. Also, under
the appropriate assumptions on the control sequences and operators, our
iterative method can be reduced to recent methods. So, the results here improve
and extend some recent corresponding results given by many other authors.
