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

Abstract

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.