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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 750473, 8 pages
http://dx.doi.org/10.1155/2013/750473
Research Article

Synchronal Algorithm and Cyclic Algorithm for Hierarchical Fixed Point Problems and Variational Inequalities

College of Science, Civil Aviation University of China, Tianjin 300300, China

Received 26 May 2013; Accepted 23 August 2013

Academic Editor: Sehie Park

Copyright © 2013 Peichao Duan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 of nonexpansive mappings and also the unique solution of a variational inequality. The results presented 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.