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Journal of Applied Mathematics
Volume 2013, Article ID 139123, 8 pages
http://dx.doi.org/10.1155/2013/139123
Research Article

New Hybrid Steepest Descent Algorithms for Equilibrium Problem and Infinitely Many Strict Pseudo-Contractions in Hilbert Spaces

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

Received 4 May 2013; Accepted 17 June 2013

Academic Editor: Gue Myung Lee

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 an explicit iterative scheme for finding a common element of the set of fixed points of infinitely many strict pseudo-contractive mappings and the set of solutions of an equilibrium problem by the general iterative method, which solves the variational inequality. In the setting of real Hilbert spaces, strong convergence theorems are proved. The results presented in this paper improve and extend the corresponding results reported by some authors recently. Furthermore, two numerical examples are given to demonstrate the effectiveness of our iterative scheme.