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

An explicit iterative method to solve generalized mixed equilibrium  problem, variational inequality problem and hierarchical fixed point problem  for a nearly nonexpansive mapping