Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 794178, 21 pages
An Iterative Algorithm Combining Viscosity Method with Parallel Method for a Generalized Equilibrium Problem and Strict Pseudocontractions
1College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
2Department of Information Management, Cheng Shiu University, Kaohsiung, Taiwan 833, Taiwan
3Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 804, Taiwan
Received 5 August 2008; Accepted 4 January 2009
Academic Editor: Hichem Ben-El-Mechaiekh
Copyright © 2009 Jian-Wen Peng et al. 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 introduce a new approximation scheme combining the viscosity method with parallel
method for finding a common element of the set of solutions of a generalized equilibrium
problem and the set of fixed points of a family of finitely strict pseudocontractions. We
obtain a strong convergence theorem for the sequences generated by these processes in Hilbert
spaces. Based on this result, we also get some new and interesting results. The results in
this paper extend and improve some well-known results in the literature.