The common solution for a generalized equilibrium problem, a variational inequality problem and a hierarchical fixed point problem

Abstract

The present paper aims to deal with a new iterative method to find a common solution of a generalized equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for a sequence of nearly nonexpansive mappings. It is proved that the proposed method converges strongly to a common solution of above problems under some assumptions. The results here improve and extend some recent corresponding results by many other authors.