  This paper deals with a modified iterative projection method for
approximating a solution of the hierarchical fixed point problem for a sequene
of nearly nonexpansive mappings with respect to a nonexpansive mapping. It is
shown that under certain approximate assumptions on the operators and
parameters, the modified iterative sequence converges strongly to a common
element of the set of the common fixed points of nearly nonexpansive
mappings.Also, this point solves some variational inequality. As a special
case, this projection method can be used to find the minimum norm solution of
the given variational inequality. The results here improve and extend some
recent corresponding results of other authors.
