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Journal of Applied Mathematics
Volume 2014, Article ID 381592, 7 pages
Research Article

Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities with -Strict Pseudocontractions

1College of Computer Science and Information Engineering, Chongqing Technology and Business University, Chongqing 400067, China
2College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Received 4 January 2014; Accepted 20 February 2014; Published 25 March 2014

Academic Editor: Jian-Wen Peng

Copyright © 2014 Qian-Fen Gong and Dao-Jun Wen. 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.


We modify the relaxed hybrid steepest-descent methods to the case of variational inequality for finding a solution over the set of common fixed points of a finite family of strictly pseudocontractive mappings. The strongly monotone property defined on cost operator was extended to relaxed cocoercive in convergence analysis. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors.