We propose synchronal algorithm and cyclic algorithm based on the general iterative method for solving a hierarchical fixed point problem. Under suitable parameters, the iterative sequence converges strongly to a common fixed point ofNnonexpansive mappings and also the unique solution of a variational inequality. The resultspresented in this paper improve and extend the corresponding results reported recently by some authors. Furthermore, a numerical example is given to demonstrate the effectiveness of our iterative schemes.
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